Question

Find the inverse of the function on the given domain.

Answer 1

To find the inverse of a function, switch the roles of x and y, solve for y, and express the inverse function explicitly.

Step-by-step explanation:

To find the inverse of a function, we switch the roles of x and y in the original function and then solve for y. Let's say the original function is y = f(x). To find the inverse, we write it as x = f^-1(y). Next, we solve for y and express the inverse function explicitly. The domain of the inverse function is the same as the range of the original function.

Answer 2

Given:

There are given that the function:

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

Step-by-step 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√(x)=y-19 \\ y=\pm√(x)+19 \\ y=√(x)+19,-√(x)+19 \end{gathered}`

Then,

`f^(-1)(x)=√(x)+19,-√(x)+19`

Final answer:

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

`f^(-1)(x)=√(x)+19`