Given the function g ( x ) = 2 x − 5 3 g\left(x\right)=\frac{2x-5}{3} g ( x ) = 3 2 x − 5 , what is g − 1 ( x ) . g^{-1}\left(x\right). g − 1 ( x ) . ?

g − 1 ( x ) = 3 x + 5 2 g^{-1}\left(x\right)=\frac{3x+5}{2} g − 1 ( x ) = 2 3 x + 5

g − 1 ( x ) = 3 x − 5 2 g^{-1}\left(x\right)=\frac{3x-5}{2} g − 1 ( x ) = 2 3 x − 5

g − 1 ( x ) = 5 x − 3 2 g^{-1}\left(x\right)=\frac{5x-3}{2} g − 1 ( x ) = 2 5 x − 3

g − 1 ( x ) = 2 x + 5 3 g^{-1}\left(x\right)=\frac{2x+5}{3} g − 1 ( x ) = 3 2 x + 5

Given the function g ( x ) = 3 x + 5 g\left(x\right)=\ 3x+5 g ( x ) = 3 x + 5 what is the inverse?

g − 1 ( x ) = x − 5 3 g^{-1}\left(x\right)=\frac{x-5}{3} g − 1 ( x ) = 3 x − 5

g − 1 ( x ) = x + 5 3 g^{-1}\left(x\right)\ =\ \frac{x+5}{3} g − 1 ( x ) = 3 x + 5

g − 1 ( x ) = x − 3 5 g^{-1}\left(x\right)=\frac{x-3}{5} g − 1 ( x ) = 5 x − 3

g − 1 ( x ) = x + 3 5 g^{-1}\left(x\right)=\frac{x+3}{5} g − 1 ( x ) = 5 x + 3

What is the inverse of the quadratic q ( x ) = x 2 + 8 x + 10 q\left(x\right)=x^{2\ }+8x\ +10 q ( x ) = x 2 + 8 x + 1 0 such that the domain is restricted x ≤ − 4 x\le-4 x ≤ − 4 ?

q − 1 ( x ) = − x + 6 − 4 q^{-1}\left(x\right)=-\sqrt{x+6}-4 q − 1 ( x ) = − x + 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 4

q − 1 ( x ) = − x − 6 + 4 q^{-1}\left(x\right)=-\sqrt{x-6}+4 q − 1 ( x ) = − x − 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 4

q − 1 ( x ) = x − 6 + 4 q^{-1}\left(x\right)=\sqrt{x-6}+4 q − 1 ( x ) = x − 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 4

q − 1 ( x ) = x + 6 − 4 q^{-1}\left(x\right)=\ \sqrt{x+6}-4 q − 1 ( x ) = x + 6 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 4

What is the inverse of the function f ( x ) = 3 ( 2 ) x − 5 f\left(x\right)=\ 3\left(2\right)^x-5 f ( x ) = 3 ( 2 ) x − 5 .

f − 1 ( x ) = log ⁡ 2 ( x + 5 3 ) f^{-1}\left(x\right)=\log_2\left(\frac{x+5}{3}\right) f − 1 ( x ) = lo g 2 ( 3 x + 5 )

f − 1 ( x ) = log ⁡ 2 ( x − 5 3 ) f^{-1}\left(x\right)=\log_2\left(\frac{x-5}{3}\right) f − 1 ( x ) = lo g 2 ( 3 x − 5 )

f − 1 ( x ) = log ⁡ 2 ( x + 3 5 ) f^{-1}\left(x\right)=\log_2\left(\frac{x+3}{5}\right) f − 1 ( x ) = lo g 2 ( 5 x + 3 )

f − 1 ( x ) = log ⁡ 2 ( 3 x 5 ) f^{-1}\left(x\right)=\log_2\left(\frac{3x}{5}\right) f − 1 ( x ) = lo g 2 ( 5 3 x )

What is the inverse of the function t ( x ) = 3 ( 2 ) ( x − 5 ) + 4 t\left(x\right)=3\left(2\right)^{\left(x-5\right)}+4 t ( x ) = 3 ( 2 ) ( x − 5 ) + 4 ?

t − 1 ( x ) = log ⁡ 2 ( x − 4 3 ) + 5 t^{-1}\left(x\right)=\log_2\left(\frac{x-4}{3}\right)+5 t − 1 ( x ) = lo g 2 ( 3 x − 4 ) + 5

t − 1 ( x ) = log ⁡ 2 ( x + 5 3 ) − 4 t^{-1}\left(x\right)=\log_2\left(\frac{x+5}{3}\right)-4 t − 1 ( x ) = lo g 2 ( 3 x + 5 ) − 4

t − 1 ( x ) = log ⁡ 2 ( x − 4 3 ) − 5 t^{-1}\left(x\right)=\log_2\left(\frac{x-4}{3}\right)-5 t − 1 ( x ) = lo g 2 ( 3 x − 4 ) − 5

t − 1 ( x ) = log ⁡ 2 ( x − 5 3 ) + 4 t^{-1}\left(x\right)=\log_2\left(\frac{x-5}{3}\right)+4 t − 1 ( x ) = lo g 2 ( 3 x − 5 ) + 4

A scientist counts 20 bacteria in an experimental culture and observes that one hour later the count is 60 bacteria. The scientist determines the model for the growth of experiment is b ( h ) = 20 ( 3 ) h b\left(h\right)=20\left(3\right)^h b ( h ) = 2 0 ( 3 ) h . What equation models the growth in minutes. Choose all that apply.

b ( m ) = 20 ( 1.0185 ) m b\left(m\right)=20\left(1.0185\right)^m b ( m ) = 2 0 ( 1 . 0 1 8 5 ) m

b ( h ) = 20 ( 3 ) 1 60 h b\left(h\right)=20\left(3\right)^{\frac{1}{60}h} b ( h ) = 2 0 ( 3 ) 6 0 1 h

b ( m ) = 20 ( 1.18 ) m b\left(m\right)=20\left(1.18\right)^m b ( m ) = 2 0 ( 1 . 1 8 ) m

b ( h ) = 20 ( 3 ) 1 24 h b\left(h\right)=20\left(3\right)^{\frac{1}{24}h} b ( h ) = 2 0 ( 3 ) 2 4 1 h

b ( t ) = 200 ( 1.02 ) t b\left(t\right)\ =\ 200\left(1.02\right)^{t\ } b ( t ) = 2 0 0 ( 1 . 0 2 ) t models the growth of a bacteria population where t represents the hours and b(t) represents the number of bacteria. Which equation models the growth of the bacteria after any given amount of days?

b ( d ) = 200 ( 1.608 ) d b\left(d\right)=200\left(1.608\right)^d b ( d ) = 2 0 0 ( 1 . 6 0 8 ) d

b ( t ) = 200 ( 1.02 ) 24 t b\left(t\right)=200\left(1.02\right)^{24t} b ( t ) = 2 0 0 ( 1 . 0 2 ) 2 4 t

b ( t ) = 200 ( 1.02 ) 1 24 t b\left(t\right)=200\left(1.02\right)^{\frac{1}{24}t} b ( t ) = 2 0 0 ( 1 . 0 2 ) 2 4 1 t

b ( d ) = 200 ( 1.0008 ) d b\left(d\right)=200\left(1.0008\right)^d b ( d ) = 2 0 0 ( 1 . 0 0 0 8 ) d

An account has a balance of $3,000. The rate in which interest accrues in 4.1% compounded monthly. How much time in years will the money need to be invested in order to have an account balance of $3,500? Choose all that apply

log ⁡ ( 1 + 0.041 12 ) 1.167 12 y e a r s \frac{\log_{\left(1+\frac{0.041}{12}\right)}1.167}{12}years 1 2 lo g ( 1 + 1 2 0 . 0 4 1 ) 1 . 1 6 7 y e a r s

1 12 log ⁡ ( 1 + 0.041 12 ) ( 3.5 3 ) y e a r s \frac{1}{12}\log_{\left(1+\frac{0.041}{12}\right)}\left(\frac{3.5}{3}\right)\ years 1 2 1 lo g ( 1 + 1 2 0 . 0 4 1 ) ( 3 3 . 5 ) y e a r s

log ⁡ 1.0034 1.167 12 y e a r s \frac{\log_{1.0034}1.167}{12}\ years 1 2 lo g 1 . 0 0 3 4 1 . 1 6 7 y e a r s

log ⁡ 1.167 1.0034 12 y e a r s \frac{\log_{1.167}1.0034}{12}years 1 2 lo g 1 . 1 6 7 1 . 0 0 3 4 y e a r s

George invests $1,000 into two separate accounts. Account A earns 8% compounded monthly.Account B earns 8.05% compounded quarterly. Which statements are true

Account B earns a lower yield as it earns 8.296% yield over the course of the year

Account A earns a higher yield as it earns 8.299% interest over the course of the year.

Account A earns a lower yielding interest rate as it interest is 8% per compounding

Account B earns a higher yiellding interest rate over the year as its interest is 8.05% per compounding

Solve the following inequality ∣ 3 x + 4 ∣ + 7 ≤ 4 \left|3x+4\right|+7\le4 ∣ 3 x + 4 ∣ + 7 ≤ 4

x ≤ − 7 3 x\le\frac{-7}{3} x ≤ 3 − 7

− 1 3 ≤ x ≤ − 7 3 -\frac{1}{3}\le x\le-\frac{7}{3} − 3 1 ≤ x ≤ − 3 7

What are the transformations that occur in the equation l ( x ) = 5 ∣ 1 3 x − 1.333 ∣ + 7 l\left(x\right)=5\left|\frac{1}{3}x-1.333\right|+7 l ( x ) = 5 ∣ ∣ ∣ ∣ 3 1 x − 1 . 3 3 3 ∣ ∣ ∣ ∣ + 7

Vertical stretch of 5, horizontal stretch of 3, translated right 4, translated up 7

vertical shrink (compression) of 5, Horizontal shrink (compression) of 3, translated right 4 and up 7

Vertical stretch of 5, horizontal stretch of 3, Translated right 1.333 and up 7.

Vertical stretch of 5, horizontal stretch of 1/3, translated right 1.333 and up 7

In order for a starbucks coffee lid to fit its cup it must have a diameter of 2.5 inches with no more than a margin of error of 1/8 inch. Which of the following is true?

∣ d − 2.5 ∣ ≤ 1 8 { 2.375 ≤ x ≤ 2.625 } \left|d-2.5\right|\le\frac{1}{8}\ \ \ \left\{\ 2.375\le x\le2.625\right\} ∣ d − 2 . 5 ∣ ≤ 8 1 { 2 . 3 7 5 ≤ x ≤ 2 . 6 2 5 }

∣ d − 2.5 ∣ ≤ . 125 { 2.4 ≤ x ≤ 2.63 } \left|d-2.5\right|\ \le.125\ \ \ \ \left\{2.4\le x\le2.63\right\} ∣ d − 2 . 5 ∣ ≤ . 1 2 5 { 2 . 4 ≤ x ≤ 2 . 6 3 }

∣ d − 1 8 ∣ ≤ 2.5 { 2.375 ≤ x ≤ 2.625 } \left|d-\frac{1}{8}\right|\le2.5\ \ \ \ \left\{2.375\le x\le2.625\right\} ∣ ∣ ∣ ∣ d − 8 1 ∣ ∣ ∣ ∣ ≤ 2 . 5 { 2 . 3 7 5 ≤ x ≤ 2 . 6 2 5 }

∣ d − . 125 ∣ ≤ 2.5 { 2.4 ≤ x ≤ 2.6 } \left|d-.125\right|\le2.5\ \ \ \ \ \left\{2.4\le x\le2.6\right\} ∣ d − . 1 2 5 ∣ ≤ 2 . 5 { 2 . 4 ≤ x ≤ 2 . 6 }

Inverses and Exponential Math 3

Quiz

•

Mathematics

•

10th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

HSF-BF.B.4A, HSF-BF.B.4D, HSF-BF.B.4C

+11

Standards-aligned

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28 questions

Show all answers

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Given the function $g\left(x\right)=\frac{2x-5}{3}$ , what is $g^{-1}\left(x\right).$ ?

$g^{-1}\left(x\right)=\frac{3x+5}{2}$

$g^{-1}\left(x\right)=\frac{3x-5}{2}$

$g^{-1}\left(x\right)=\frac{5x-3}{2}$

$g^{-1}\left(x\right)=\frac{2x+5}{3}$

Tags

CCSS.HSF-BF.B.4A

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Given the function $g\left(x\right)=\ 3x+5$ what is the inverse?

$g^{-1}\left(x\right)\ =\ \frac{x+5}{3}$

$g^{-1}\left(x\right)=\frac{x-5}{3}$

$g^{-1}\left(x\right)=\frac{x-3}{5}$

$g^{-1}\left(x\right)=\frac{x+3}{5}$

Tags

CCSS.HSF-BF.B.4A

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The function W(n)= 32-0.05n represents the volume of water Andrei uses (in liters) if he uses. W(n) represents the volume and n represents the number of liters

What is the inverse and what is the meaning of the inverse equations

$w^{-1}\left(n\right)=-20n+640$ such that $w^{-1}\left(n\right)$ is the volume of the water and n is the number of liters

$w^{-1}\left(n\right)=-20n+640$ such that $w^{-1}\left(n\right)$ is the number of liters and n represents the volume of water

$w^{-1}\left(n\right)=-n+640$ such that $w^{-1}\left(n\right)$ is the number of liters and n represents the volume of water

$w^{-1}\left(n\right)\ =-\ n+640\$ such that $w^{-1}\left(n\right)$ is the volume of water and n is the number of liters

Tags

CCSS.HSF-BF.B.4A

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If g(x) and f(x) are inverses, what are the points of f(x) if g(x) = {(1,2), (3,5), (-2,8)}.

f(x) = {(1,2), (3,5), (-2,8)}

f(x) = {(2,1), (3,5), (8,-2)}

f(x) = {(2,1), (5,3), (8,-2)}

f(x)= {(1,2) , (3,5), (-2,8)}

Tags

CCSS.HSF-BF.B.4C

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following graphs shows to functions that are Linear Inverse functions?

Tags

CCSS.HSF-BF.B.4C

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

True or False. The following graph shows two functions that are not inverses.

True

False

Tags

CCSS.HSF-BF.B.4B

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Determine the inverse of $f\left(x\right)\ =\ x^2-8$ with a restricted domain of $x\ge0$

$f^{-1}\left(x\right)=\ \sqrt{x+8}$

$f^{-1}\left(x\right)=-\sqrt{x+8}$

$f^{-1}\left(x\right)=\sqrt{x-8}$

$f^{-1}\left(x\right)=-\sqrt{x-8}$

Tags

CCSS.HSF-BF.B.4D

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Determine the inverse of $f\left(x\right)\ =\ x^2-8$ with a restricted domain of $x\le0$

$f^{-1}\left(x\right)=\ \sqrt{x+8}$

$f^{-1}\left(x\right)=-\sqrt{x+8}$

$f^{-1}\left(x\right)=\sqrt{x-8}$

$f^{-1}\left(x\right)=-\sqrt{x-8}$

Tags

CCSS.HSF-BF.B.4D

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the inverse of the quadratic $q\left(x\right)=x^{2\ }+8x\ +10$ such that the domain is restricted $x\le-4$ ?

$q^{-1}\left(x\right)=-\sqrt{x-6}+4$

$q^{-1}\left(x\right)=\sqrt{x-6}+4$

$q^{-1}\left(x\right)=\ \sqrt{x+6}-4$

$q^{-1}\left(x\right)=-\sqrt{x+6}-4$

Tags

CCSS.HSF-BF.B.4D

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the inverse of the quadratic $t\left(x\right)=3x^2-12x\ +4$ such that the domain is restricted $x\ge2$ ?

$t^{-1}\left(x\right)=-\sqrt{\frac{x-8}{3}}+2$

$t^{-1}\left(x\right)=\sqrt{\frac{x-8}{3}}+2$

$t^{-1}\left(x\right)=-\sqrt{\frac{x+8}{3}}+2$

$t^{-1}\left(x\right)=\sqrt{\frac{x+8}{3}}+2$

Tags

CCSS.HSF-BF.B.4D

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28 questions

Given the function g(x)=2x−53g\left(x\right)=\frac{2x-5}{3}g(x)=32x−5​ , what is g−1(x).g^{-1}\left(x\right).g−1(x). ?

Given the function g(x)= 3x+5g\left(x\right)=\ 3x+5g(x)= 3x+5 what is the inverse?

The function W(n)= 32-0.05n represents the volume of water Andrei uses (in liters) if he uses. W(n) represents the volume and n represents the number of liters What is the inverse and what is the meaning of the inverse equations

If g(x) and f(x) are inverses, what are the points of f(x) if g(x) = {(1,2), (3,5), (-2,8)}.

Which of the following graphs shows to functions that are Linear Inverse functions?

True or False. The following graph shows two functions that are not inverses.

Determine the inverse of f(x) = x2−8f\left(x\right)\ =\ x^2-8f(x) = x2−8 with a restricted domain of x≥0x\ge0x≥0

Determine the inverse of f(x) = x2−8f\left(x\right)\ =\ x^2-8f(x) = x2−8 with a restricted domain of x≤0x\le0x≤0

What is the inverse of the quadratic q(x)=x2 +8x +10q\left(x\right)=x^{2\ }+8x\ +10q(x)=x2 +8x +10 such that the domain is restricted x≤−4x\le-4x≤−4 ?

What is the inverse of the quadratic t(x)=3x2−12x +4t\left(x\right)=3x^2-12x\ +4t(x)=3x2−12x +4 such that the domain is restricted x≥2x\ge2x≥2 ?

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Given the function $g\left(x\right)=\frac{2x-5}{3}$ , what is $g^{-1}\left(x\right).$ ?

Given the function $g\left(x\right)=\ 3x+5$ what is the inverse?

The function W(n)= 32-0.05n represents the volume of water Andrei uses (in liters) if he uses. W(n) represents the volume and n represents the number of liters

What is the inverse and what is the meaning of the inverse equations

Determine the inverse of $f\left(x\right)\ =\ x^2-8$ with a restricted domain of $x\ge0$

Determine the inverse of $f\left(x\right)\ =\ x^2-8$ with a restricted domain of $x\le0$

What is the inverse of the quadratic $q\left(x\right)=x^{2\ }+8x\ +10$ such that the domain is restricted $x\le-4$ ?

What is the inverse of the quadratic $t\left(x\right)=3x^2-12x\ +4$ such that the domain is restricted $x\ge2$ ?