Question

F(x) and g(x) are inverse functions. What is g(f(-4)) equal to?

Answer 1

1/f(-4) should be the answer

Answer 2

`g(f(-4))=-4`.

Explanation:

An inverse function is a function that will “undo” anything that the original function does. For example, if a function takes a to b, then the inverse must take b to a.

These are the conditions for two functions
`f` and
`g` to be inverses:

• 
  `f(g(x))=x` for all
  `x` in the domain of
  `g`

• 
  `g(f(x))=x` for all
  `x` in the domain of
  `f`

This is because if
`f(x)` and
`g(x)` are inverses, composing
`f(x)` and
`g(x)` (in either order) creates the function that for every input returns that input. This is known as “the identity function".

We know that
`f(x)` and
`g(x)` are inverse functions and according with the above information we get that:

`g(f(-4))=-4`