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Question

Explain how you can tell that f(x) = x³ and  are inverse functions.

List two more functions that are inverses of each other.

Answer 1

We can check that they are inverses by computing the composition f(g(x)) or g(f(x)). Being inverses, f(g(x)) = x = g(f(x)) should always be true.

Let f(x) = x³ and g(x) = ³√x. Then, f(g(x)) = (³√x)³ = x and g(f(x)) = ³√(x³) = x.

Let f(x) = xⁿ and g(x) = ⁿ√x. For any natural number n, f(x) and g(x) are inverses. Choose two values of n and you have two more function/inverse pairs.