Chapter 3.4, Problem 45E

To determine

To write:an equation for every translated graph.

Answer to Problem 45E

  $\begin{array}{c}f\left(x\right)={\left(x-6\right)}^2-5\\ f^{-1}\left(x\right)=\sqrt{x+5}+6\end{array}$

Explanation of Solution

Given information:

Parent function, $y=x^2$

Inverse of parent function, $y=\pm x$

First translation: The parent function is translated 6 units right and 5 units down.

Second translation: Inverse of parent function is translated to get the inverse of translated function.

Calculation:

The inverse of translated parent function will be reversal of both direction and values, i.e. 5 units left and 6 units up.

Thus, the equation for parent function translation will be $f\left(x\right)={\left(x-6\right)}^2-5$ and the equation for inverse translation function will be $f^{-1}\left(x\right)=\sqrt{x+5}+6$ .