Refer to the functions $$ f, g $$, and $$ h $$ and find the given function. $$ f(x)=3 x+5 $$ $$ g(x)=x^{2} $$ $$ (f \circ g \circ h)(x)=\square $$

Question

UpStudy AI · Accepted Answer

We need to compute the composition

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

**Step 1. Apply $$ g $$ to $$ h(x) $$:**

Since

$$
g(x) = x^2,
$$

we have

$$
g(h(x)) = (h(x))^2.
$$

**Step 2. Apply $$ f $$ to $$ g(h(x)) $$:**

Given

$$
f(x) = 3x + 5,
$$

substitute $$ x = (h(x))^2 $$ into $$ f $$:

$$
f\bigl((h(x))^2\bigr) = 3 \,(h(x))^2 + 5.
$$

Thus, the composite function is

$$
(f \circ g \circ h)(x) = 3 \,(h(x))^2 + 5.
$$
$$ (f \circ g \circ h)(x) = 3 \, (h(x))^2 + 5 $$

Refer to the functions \( f, g \), and \( h \) and find the given function. \[ f(x)=3 x+5 \] \[ g(x)=x^{2} \] \( (f \circ g \circ h)(x)=\square \)