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)=x^2
g(x)=□

Explanation:

Step1: Recall function composition

$(f \circ g)(x) = f(g(x))$

Step2: Match to given $h(x)$

We know $f(x)=x^2$, so substitute $g(x)$ into $f$: $f(g(x))=(g(x))^2$. Since $h(x)=(6x-9)^2$, set $(g(x))^2=(6x-9)^2$.

Step3: Solve for $g(x)$

Take the "inside" function as $g(x)$: $g(x)=6x-9$

Answer:

$g(x)=6x-9$