If F(x) and G(x) are two functions such that F(G(x)) = x then F(x) and G(x) are ..?

They are inverse functions though to be completely thorough your teacher should have also put g(f(x)) = x as well. Though I can see what your teacher is aiming for at least.

The idea is that whatever the output of g(x) is, it's plugged into f(x) and the initial input is the result. So g(x) takes a step forward and f(x) takes a step back undoing everything g(x) did. Which is exactly what an inverse operation does.

AmitPaswan AmitPaswan · Answer 2 · 2022-07-20T12:27:38+02:00

The F(x) and G(x) are inverse function .

What is inverse function?

Inverse function is represented by f⁻¹ with regards to the original function f and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.

According to the question

F(x) and G(x) are two functions .

and F(G(x)) = x

i.e

result of G(x) is put under F(x)

As we know

According to the inverse function

the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function.

Here , G(x) = domain of F(x)

i.e

x of F(x) = G(x)

x = G(x)

i.e

range of G(x) is x .

and domain of F(x) = G(x) = x

Therefore ,

F(x) and G(x) are inverse of each other .

Hence, The F(x) and G(x) are inverse function .

To know more about inverse function here:

https://brainly.com/question/2541698

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