Question

Find and simplify expressions for f(g(x)) and g(f(x)) where f(x)=e^(2x) and g(x)=ln(x). What is f(g(x)) and g(f(x))?

Answer 1

f(g(x)) = e^(2*ln(x)) = e^(ln(x^2)) = x^2

g(f(x)) = ln(e^(2x)) = 2x