Express f(x)=2^x as the composition of two elementary functions

Answer 1

Probably they mean using a function like exp(x) also known as e^x.

Recall e^ln(2) = 2 (by definition of natural log.

So exp( ln(2) * x) = 2^x (study your log identities!)

So compose g(h(x)) with h(z)= z*ln(2), g(z) = exp(z) (I could have written any letter instead of z).

Answer 2

One of possible solutions: g(x) = 2x & h(x) = 2^x-1.

Then (g_°h)(x) = g(f(x)) = 2·h(x) = 2·2^x-1= 2^x = f(x)