For each pair of functions f and g below, find f(g(x)) and g(f(x)). Then, determine whether f and g are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all x in the domain ofthe composition.
You do not have to indicate the domain.)

a)  f(g(x)) = = = x

    g(f(x)) = = = x

    f and g are inverses

b)   f(g(x)) = x + 3 + 3 = x + 6

     g(f(x)) = x + 3 + 3 = x + 6

     f and g are not inverses

Step-by-step explanation:

a)

f(g(x)) = = = x

g(f(x)) = = = x

Since f(g(x)) = g(f(x)) = x, then f and g are inverses

b)

f(g(x)) = x + 3 + 3 = x + 6

g(f(x)) = x + 3 + 3 = x + 6

Since f(g(x)) = g(f(x)) ≠ x, then f and g are not inverses

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step-by-step explanation:

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