Question

Express the function y=5(x−6)² as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x).

Answer 1

y = 5u², u=x-6

Explanation:

Given the function:

`y=5(x-6)^2`

We want to express f(x) as a composition of two functions.

Let u = x-6

`\implies y=5u^2`

Therefore, the function y=5(x−6)² as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x)

`\begin{gathered} y=5u^2\text{ where:} \\ f(u)=5u^2 \\ u=g(x)=x-6 \end{gathered}`