Respuesta :

Answer:

Inverse function: The function f(x) goes from domain to range and the inverse function [tex]f^{-1}[/tex] goes from Range to domain

i.,e [tex]f(f^{-1}(x)) = f^{-1}(f(x)) = x[/tex]

As per the given statement:

if h(x) is the inverse of f(x)

by definition:

[tex]h(x) = f^{-1}(x)[/tex]

then;

[tex]h(f(x)) = f^{-1}(f(x)) =(f^{-1}f)(x) = x[/tex]

Therefore, the value of h(f(x)) is x.

abidemiokin

If h(x) is the inverse of g(x), the the composite function h(g(x)) is x

Given the function h(x) and g(x). If h(x) is the inverse of f(x), this can be expressed as:

[tex]h(x)=g^{-1}x[/tex] ................................. 1

We are to get the composite function h(g(x))

Substitute equation 1 into the composite function to have:

[tex]h(g^{-1}(x))=g(g^{-1}(x)) = x[/tex]

Hence if h(x) is the inverse of g(x), the the composite function h(g(x)) is x

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