Composition & Inverse Review Quiz

Mathematics

11th Grade

CCSS covered

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14 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Given the functions
$f\left(x\right)=x^2-3$ and $g\left(x\right)=\sqrt{x-5}$
find $f\circ g$

$\sqrt{x^2-8}$

$x-8$

$\sqrt{x^2+2}$

$x-2$

Answer explanation

Tags

CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Find the inverse of the function.

f^-1 = x³ − 5

f^-1 = x³ + 15

f^-1 = x³ + 5

Inverse does not exist

Tags

CCSS.HSF-BF.B.4A

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What is the inverse of the function?

$f^{-1}\left(x\right)=\ \left(\frac{x-9}{3}\right)^3$

$f^{-1}\left(x\right)=\ \left(\frac{x-3}{9}\right)^3$

$f^{-1}\left(x\right)=^3\sqrt{\frac{x-9}{3}}$

$f^{-1}\left(x\right)=^3\sqrt{x-9}+3$

Tags

CCSS.HSF-BF.B.4A

OPEN ENDED QUESTION

5 mins • 1 pt

Given
$f\left(x\right)=2x^2-5x$
$g\left(x\right)=3x^2$
Evaluate $f\left(g\left(2\right)\right)$

Evaluate responses using AI:

OFF

Tags

CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Determine the value of x given f(x) = 10

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

What is the value of f(0)?

-2

Tags

CCSS.HSF.IF.A.2

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

Which is f ^-1(x)?

f^-1(x) = 5x + 3

f^-1(x) = 5x - 3

f^-1(x) = 5x - 15

f^-1(x) = 1/5(x) + 3/5

Tags

CCSS.HSF-BF.B.4A

10.

DRAG AND DROP QUESTION

1 min • 1 pt

Use the table to answer the following:
$f^{-1}\left(1\right)$ $+$ $f\left(-14\right)$ $=$ (a)
$f^{-1}\left(-2\right)=$ (b)

$20$

$10$

Tags

CCSS.HSF-BF.B.4C

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11th Grade

Composition & Inverse Review

Given the functions f(x)=x2−3f\left(x\right)=x^2-3f(x)=x2−3 and g(x)=x−5g\left(x\right)=\sqrt{x-5}g(x)=x−5​ find f∘gf\circ gf∘g

Find the inverse of the function.

What is the inverse of the function?

Given f(x)=2x2−5xf\left(x\right)=2x^2-5xf(x)=2x2−5x g(x)=3x2g\left(x\right)=3x^2g(x)=3x2 Evaluate f(g(2))f\left(g\left(2\right)\right)f(g(2))

Determine the value of x given f(x) = 10

What is the value of f(0)?

Which is f -1(x)?

are these inverse functions?

Use the table to answer the following: f−1(1)f^{-1}\left(1\right)f−1(1) +++ f(−14)f\left(-14\right)f(−14) === ​ (a) f−1(−2)=f^{-1}\left(-2\right)=f−1(−2)= ​ ​ (b)

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Given the functions
$f\left(x\right)=x^2-3$ and $g\left(x\right)=\sqrt{x-5}$
find $f\circ g$

Given
$f\left(x\right)=2x^2-5x$
$g\left(x\right)=3x^2$
Evaluate $f\left(g\left(2\right)\right)$

Which is f ^-1(x)?

Use the table to answer the following:
$f^{-1}\left(1\right)$ $+$ $f\left(-14\right)$ $=$ (a)
$f^{-1}\left(-2\right)=$ (b)