Question

Inverse Questions. Pls Help give answer options. A,B,C, or D.

Answer 1

The Solution:

GIven:

Required:

Find the inverse of the function and its domain.

Step 1:

Let:

`\begin{gathered} y=f(x)=√(x)-5 \\ \\ y=√(x)-5 \end{gathered}`

Step 2:

`y+5=√(x)`
`\begin{gathered} (y+5)^2=(√(x))^2 \\ \\ (y+5)^2=x \\ \\ x=(y+5)^2 \end{gathered}`

Replace y with x.

`f^(-1)(x)=(x+5)^2=x^2+10x+25`

Answer: [option C]

`\begin{gathered} Inverse:\text{ }f^(-1)(x)=x^2+10x+25 \\ \\ Domain:\text{ \lbrack0},\infty) \end{gathered}`