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Answer:

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

i.,e \(f(f^{-1}(x)) = f^{-1}(f(x)) = x\)

As per the given statement:

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

by definition:

\(h(x) = f^{-1}(x)\)

then;

\(h(f(x)) = f^{-1}(f(x)) =(f^{-1}f)(x) = x\)

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:

\(h(x)=g^{-1}x\) ................................. 1

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

Substitute equation 1 into the composite function to have:

\(h(g^{-1}(x))=g(g^{-1}(x)) = x\)

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

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