Question

Question #23f3c

Answer 1

Assuming that, by f-1(x) you mean `f^(-1)(x)` (the inverse of `f(x)`) then the answers are `1` and `4`, respectively.

Explanation:

Let's first review the process of finding inverses. It consists of 4 steps:

1. Change `f(x)` to `y`.
2. Switch `x` and `y`.
3. Solve for `y`.
4. Change `y` to `f^(-1)(x).`

As this method applies to `f(x)=2x+2`, we have:
`y=2x+2=>` Changing `f(x)` to `y`
`x=2y+2=>` Switching `x` and `y`
`x-2=2y->y=(x-2)/2=>` Solving for `y`
`f^(-1)(x)=(x-2)/2=>` Changing `y` to `f^(-1)(x)`

The question asks for `f^(-1)(x)` when `x=4`, so:
`f^(-1)(x)=(x-2)/2`
`->f^(-1)(x)=(4-2)/2`
`->f^(-1)(x)=1`

The correct answer, then, is `1`.

We follow the same process for `f(x)=2x-6`:
`y=2x-6`
`x=2y-6`
`2y=x+6`
`y=(x+6)/2->f^(-1)(x)=(x+6)/2`

Now we just plug in `2` for `x` and do the math:
`f^(-1)(x)=(x+6)/2`
`->f^(-1)(x)=(2+6)/2`
`->f^(-1)(x)=4`

The correct answer for this problem is `4`.