Question

practice assignment 3.4 composition of functions score: 50/80 answered: 5/8 question 6 the function ( h(x) = (x + 2)^2 ) can be expressed in the form ( f(g(x)) ), where ( f(x) = x^2 ), and ( g(x) ) is defined below: ( g(x) = ) question help: ( square ) video ( square ) message instructor

Explanation:

Step1: Identify composite function structure

We know $h(x) = f(g(x))$, with $f(x)=x^2$ and $h(x)=(x+2)^2$.

Step2: Substitute $g(x)$ into $f(x)$

Set $f(g(x)) = (g(x))^2$. We equate this to $h(x)=(x+2)^2$, so $(g(x))^2=(x+2)^2$.

Step3: Solve for $g(x)$

Take the "inner function" that when squared gives $(x+2)^2$, so $g(x)=x+2$.

Answer:

$g(x) = x + 2$