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

Answer:

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

Step-by-step 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:

$g(f(-4))=-4$