Answer:
[tex]g(f(-4))=-4[/tex].
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 [tex]f[/tex] and [tex]g[/tex] to be inverses:
- [tex]f(g(x))=x[/tex] for all [tex]x[/tex] in the domain of [tex]g[/tex]
- [tex]g(f(x))=x[/tex] for all [tex]x[/tex] in the domain of [tex]f[/tex]
This is because if [tex]f(x)[/tex] and [tex]g(x)[/tex] are inverses, composing [tex]f(x)[/tex] and [tex]g(x)[/tex] (in either order) creates the function that for every input returns that input. This is known as “the identity function".
We know that [tex]f(x)[/tex] and [tex]g(x)[/tex] are inverse functions and according with the above information we get that:
[tex]g(f(-4))=-4[/tex]
