Question

Find the inverse of the function on the given domain.

Answer 1

Given:

There are given that the function:

$f(x)=(x-19)^2$

Explanation:

According to the question:

We need to find the inverse of the function.

Then,

To find the inverse, first exchange f(x) into y:

So,

$\begin{gathered} f(x)=(x-19)^{2} \\ y=(x-19)^2...(1) \end{gathered}$

Then,

We need to exchange x into y:

So,

$\begin{gathered} y=(x-19)^2 \\ x=(y-19)^2...(2) \end{gathered}$

Then,

We need findthe value for y:

$\begin{gathered} \begin{equation*} x=(y-19)^2 \end{equation*} \\ \pm\sqrt{x}=y-19 \\ y=\pm\sqrt{x}+19 \\ y=\sqrt{x}+19,-\sqrt{x}+19 \end{gathered}$

Then,

$f^{-1}(x)=\sqrt{x}+19,-\sqrt{x}+19$

Final answer:

Hence, the inverse of the given function is show below:

$f^{-1}(x)=\sqrt{x}+19$