Question

Which function is the inverse of fix) = V5767O A.(-40) =3622 + 2. for = > 0O B.1-1(0) =652 + 2, for = ≥ 0O C.+ 2. for I > 0O D.f-11) = 6522. for r > 0

Answer 1

Given:

The function is

`f(x)=(√(x-2))/(6)`

Required:

Find the inverse of the function.

Step-by-step explanation:

The given function is:

`f(x)=(√(x-2))/(6)`

Put

`f(x)=y`
`y=(√(x-2))/(6)`

Interchange x and y.

`x=(√(y-2))/(6)`

Take the square on both sides.

`x^2=(y-2)/(36)`
`\begin{gathered} 36x^2=y-2 \\ y=36x^2+2 \end{gathered}`

Substitute

`y=f^(-1)(x)`
`f^(-1)(x)=36x^2+2`

Final Answer:

Option A is the correct answer.