Question

The question and answer choices are shown in the picture. Thanks.

Answer 1

The function given is,

`f(x)=(x-1)^2-4`

Given that

`y=f(x)`

Therefore,

`y=(x-1)^2-4`

Replace x with y

`x=(y-1)^2-4`

Solve for y

`\begin{gathered} x+4=(y-1_{})^2 \\ \end{gathered}`

Square-rooting both sides

`\begin{gathered} \pm\sqrt[]{x+4}=\sqrt[]{(y-1)^2} \\ \pm\sqrt[]{x+4}=y-1 \end{gathered}`

Add 1 to both sides

`\begin{gathered} \pm\sqrt[]{x+4}+1=y-1+1 \\ \pm\sqrt[]{x+4}+1=y \\ \Rightarrow y=\pm\sqrt[]{x+4}+1 \end{gathered}`

Hence,

`f^(-1)(x)=\pm\sqrt[]{x+4}+1`

The domain of the inverse function will be,

`x\ge-4`

The correct answer is Option B.