Verify that these two are inverses using composition of functions and show your work

f(g(x)) = g(f(x)) = x

Step-by-step explanation:

To prove two functions, say f(x) and g(x) are inverses to each other, we take the composition of the two functions: f(g(x)) and g(f(x)) and prove that:

                       f(g(x)) = g(f(x)) = x, x is the identity function

Now, given:

        and          

Calculate: f(g(x)):

It means to substitute in place of x.

Therefore, we get:

           = x, the identity function.

Now compute g(f(x))

Now,

                      = x

We have proved f(g(x)) = g(f(x)) = x. Hence, they are inverses of each other.

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step-by-step explanation: