Question

express the given function h as a composition of two functions f and g so that h(x)=(f∘g)(x), where one of the functions is 6x - 9. h(x)=(6x - 9)² f(x)=□

Explanation:

Step1: Identify inner function g(x)

Given the inner function is $g(x)=6x-9$.

Step2: Define outer function f(x)

The outer function takes the input and squares it, so $f(x)=x^2$.

Step3: Verify composition

$(f\circ g)(x)=f(g(x))=f(6x-9)=(6x-9)^2=h(x)$

Answer:

$f(x)=x^2$