Question

Question #29f86

Answer 1

`f^-1(-12) = -8`

Explanation:

The inverse of a function, `f^-1(y)`, reverses what the function, `f(x)`, does.

If `y = f(x)`, then `f^-1(y)=x`

Making this fit the context of your question

We are given that `f(-8) = -12`

The standard notation is `y = f(x)`, therefore, `y =-12` in this case. Then, using `f^-1(y) = x` gives us `f^-1(-12) = -8`

Answer 2

You would figure out `f(x)`, then find `f(-12)` and raise it to the `-1` power, a.k.a. find the reciprocal.

Explanation:

If `f(-8)=-12`, then what is `f(x)`? Well, `-8-4 = -12`, so `f(x)=x-4`. Then if `x=-12`, `f(x)=x-4 = f(-12)= -12-4 = -16`, so `f(-12)= -16`. Are we done? Nope. We are asked to find `f^-1(-12)`, not just `f(-12)`. That means we raise `f(-12)` to the power of `-1`.When you raise something to the `-1` power, you find the reciprocal. This is easy: just turn it into a fraction and flip it. `-16= -16/1`. Flip the fraction and you get `-1/16`. So if `f(-8)=-12`, then

`f^-1(-12)=-16`. We have our answer.