Unit 1 Review

The compositions for two pairs of functions are shown below.

Pair 1: f(x) = 3x + 6; g(x) = x/3- 2

f(g(x)) = 3(x/3- 2) + 6 = x

g(f(x)) = (3x + 6)/3- 2 = x

Pair 2: f(x) = 5x; g(x) = -5x

f(g(x)) = 5(-5x) = -25x

g(f(x)) = -5(5x) = -25x

What can you determine about Pair 1 and Pair 2 based on their compositions?

• Both pairs are inverses because f(g(x)) = g(f(x))

• Only pair 1 is an inverse because f(g(x)) = x

• Only pair 2 is an inverse because f(x) is the negative of g(x)

• Nothing can be determined.

Tags

CCSS.HSF-BF.B.4B

Lain wants to show that the following functions are inverse functions using composition. f(x) = x + 5 g(x) = x - 5

What should f ○ g and g ○ f equal if the functions are inverses of each other?

• 2x

• x

• x²

• 0

Tags

CCSS.HSF-BF.B.4B

For the functions $f\left(x\right)\ =\ x^2\ -4$  and

 $g\left(x\right)=\sqrt{x\ +\ 4}$  Which one of these verifies that these two equations are inverses of each other.

•   $f\left(x\right)\ -\ g\left(x\right)\ =\ x^2-4-\sqrt{x+4}$  

•  $f\left(x\right)\ \cdot\ g\left(x\right)\ =\ \left(x^2-4\right)\cdot\sqrt{x+4}$  

•  $f\left(g\left(x\right)\right)\ =\ x$  

•  $\frac{f\left(x\right)}{g\left(x\right)}=\frac{x^2+4}{\sqrt{x-4}}$  

Tags

CCSS.HSF-BF.B.4B

Which one of these is the equation for this graph?

• $y=\ ^3\sqrt{x}$

• $y\ =\ \sqrt{x}$

• $y\ =\ x^3$

• $y\ =\ \left|x\right|$

Tags

CCSS.HSF-IF.C.7B

Which one of these is the equation for this graph?

• $y=\ ^3\sqrt{x}$

• $y\ =\ \sqrt{x}$

• $y\ =\ x^3$

• $y\ =\ \left|x\right|$

Tags

CCSS.HSF-IF.C.7B

Which one of these is the equation for this graph?

• $y=\ ^3\sqrt{x}$

• $y\ =\ \sqrt{x}$

• $y\ =\ \frac{1}{x}$

• $y\ =\ \left|x\right|$

Tags

CCSS.HSF-IF.C.7B

A function is defined by the equation f(x) = 5x + 8

What equation represents the inverse of this function?

• $f^{-1}\left(x\right)=\frac{x-8}{5}$

• $f^{-1}\left(x\right)=5x\ -\ 8$

• $f^{-1}\left(x\right)=\frac{x+5}{8}$

• $f^{-1}\left(x\right)=\frac{1}{5x+8}$

Tags

CCSS.HSF-BF.B.4A

The point (-2, 3) lies on the graph of the function, f(x). What point lies on the graph of f ^-1(x) the function’s inverse?

• (3, -2)

• (-3, 2)

• (2, -3)

• (-2, 3)

Tags

CCSS.HSF-BF.B.4C

What equation represents the inverse f ^-1(x) of f(x) = x³ + 4

• $f^{-1}\left(x\right)=\ ^3\sqrt{x-4}$

• $f^{-1}\left(x\right)\ =\ x^3-4$

• $f^{-1}\left(x\right)=\frac{1}{x^3+4}$

• $f^{-1}\left(x\right)\ =\ 4\ -\ x^3$

Tags

CCSS.HSF-BF.B.4A

A function is defined by $y\ =\ \sqrt{x+7}$  

What equation represents the inverse of this function?

•  $y\ =\ x^2-7$  

•  $y\ =\ \left(x\ -\ 7\right)^2$  

•  $y\ =\ \frac{1}{\sqrt{x+7}}$  

•  $y\ =\ \frac{1}{x^2-7}$  

Tags

CCSS.HSF-BF.B.4A