Question

Select one the restricted domains of f(x)=(8−2x)2 that will make the inverse of f(x) a function. There may be more than one.

Answer 1

`x\leq 4` or
`x\geq 4`

Explanation:

We are given that

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

We have to find the restricted domain of f which make the inverse of f.

Substitute x=4

`f(4)=0`

One-to-one function:

The function is called one-to-one when

`f(x_1)=f(x_2)` for
`x_1=x_2`

The function is one-to-one when
`x\leq 4` or
`x\geq 4`

When the function is one-to-one then the function has inverse function.

If the function is not one-to-one then function has no inverse .

Therefore, the restricted domain of f which make the inverse of f(x) a function is given by

`x\leq 4` or
`x\geq 4`