Question

Find the inverse of the function on the given domain. f(x)=(x−8)2, [8,∞)

Answer 1

Given:

`f(x)=(x-8)^2`

Solve for inverse function:

the value of x and y interchange and slove for y

`\begin{gathered} f(x)=y \\ y=(x-8)^2 \\ x\rightarrow y \\ y\rightarrow x \\ x=(y-8)^2 \\ y-8=\sqrt[]{x} \\ y=\sqrt[]{x}+8 \end{gathered}`

Domain: Domain of function is define as a all possible input so.

`\begin{gathered} y=\sqrt[]{x}+8 \\ x\ge0 \end{gathered}`