7-7 Review - Inverse Functions

f(x) contains the points (1, 4) and (4, 6).

What points must f^-1(x) contain?

• (1, 4) and (4, 6)

• (-4, -1) and (-6, -4)

• (-1, -4) and (-4, -6)

• (4, 1) and (6, 4)

Find the inverse of  $f\left(x\right)=x^3-5$  .

•  $f^{-1}\left(x\right)\ =\ \ ^3\sqrt{x+5}$  

•  $f^{-1}\left(x\right)\ =\ ^{\ 3}\sqrt{x-5}$  

•  $f^{-1}\left(x\right)\ =\ \ ^3\sqrt{x}+5$  

•  $f^{-1}\left(x\right)\ =\ \ ^3\sqrt{x}-5$  

Identify the correct description.

• No, they are not inverses.

• Yes, they are inverses.

Find the inverse of the relation  $y=\pm\sqrt{x+3},\ x\ge-3$  .

•  $y=\left(x+3\right)^2$  

•  $y=\left(x-3\right)^2$  

•  $y=x^2-3$  

•  $y=x^2+3$  

Given: functions f(x) and g(x)

Which of the following statements is always true?

• If f(g(x)) = x, then f(x) and g(x) are inverses.

• If g(f(x)) = x, then f(x) and g(x) are inverses.

• If f(g(x)) = x and g(f(x))=x, then f(x) and g(x) are inverses.

TRUE or FALSE
The inverse of  $f\left(x\right)=x^2$   is  $g\left(x\right)=\sqrt{x}$ .

• TRUE

• FALSE

Are these inverse functions?

• No

• Yes

Find the inverse of  $f\left(x\right)\ =\ \ ^3\sqrt{x+4}-2$  

•  $f^{-1}\left(x\right)=\left(x-2\right)^3+4$  

•  $f^{-1}\left(x\right)=\left(x+2\right)^3-4$ 

•  $f^{-1}\left(x\right)=\left(x+4\right)^3-2$ 

•  $f^{-1}\left(x\right)=\left(x-4\right)^3+2$  

If the domain of  $f\left(x\right)$   is $\left[4,\ \infty\right)$ ,  then the ____ of ____ is  $\left[4,\ \infty\right)$ .

• domain,  $f^{-1}\left(x\right)$  

• range,  $f^{-1}\left(x\right)$  

• range,  $f\left(x\right)$  

Find the inverse of  $f\left(x\right)=x^2-1$  . 

•  $f^{-1}\left(x\right)=\pm\sqrt{x+1},\ x\ge-1$ 

•   $f^{-1}\left(x\right)=\pm\sqrt{x-1},\ x\ge1$ 

•  $f^{-1}\left(x\right)=\pm\sqrt{x}-1,\ x\ge0$  

•  $f^{-1}\left(x\right)=\pm\sqrt{x}+1,\ x\ge0$