If the composite functions f(g(x)) and g(f(x)) both equal x, then the function g is the____function of f.

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16-08-2022
Mathematics

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If the composite functions f(g(x)) and g(f(x)) both equal x, then the function g is the____function of f.

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Tutorconsortium366 Tutorconsortium366 · Answer 1 · 2022-08-20T04:40:07-04:00

If the composite functions f(g(x)) and g(f(x)) both equal to x, then the function g is the Inverse function of f.

What is the inverse of a function?

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.

Let us take the Example.

Suppose f(x)= x/4 and g(x)=4x.

Let x=1

then f(g(x))= f(g(1))=f(4)=1

and g(f(x))=g(f(1))=g(1/4)=1

Here, f(g(x))=g(f(x))=1

Therefore , we can say that f(g(x)) and g(f(x)) are inverse of each other.

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