Question

find (f ∘ g)(x) and (g ∘ f)(x) and graph each of these functions.
f(x) = -8x
g(x) = cot x

find (f ∘ g)(x).
(f ∘ g)(x) = \square

Explanation:

Step1: Define composite function

Recall that $(f \circ g)(x) = f(g(x))$.

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

Replace $x$ in $f(x) = -8x$ with $g(x) = \cot x$.
$$(f \circ g)(x) = -8 \cdot g(x)$$

Step3: Final substitution

Substitute $g(x)=\cot x$ into the expression.
$$(f \circ g)(x) = -8\cot x$$

Answer:

$\boldsymbol{-8\cot x}$