Final answer:
To represent the function y=(4x+2)⁵ as a composition f[g(x)], define g(x) as 4x+2 and f(u) as u⁵. Then, the composition is f(4x+2)=(4x+2)⁵.
Step-by-step explanation:
To write the function y=(4x+2)⁵ as a composition of two functions f[g(x)], we can define two different functions g(x) and f(u), where u is the output of g(x). Consider the inner function g(x) as the function inside the exponentiation, that is g(x)=4x+2. Then define the outer function f(u) as the exponentiation operation, thus f(u)=u⁵. The composition f[g(x)] is then the outer function f acting on the result of the inner function g, which gives us the original function: f[g(x)]=f(4x+2)=(4x+2)⁵.