Question

For the following exercises, find (f ∘ g)(x) and (g ∘ f)(x) for each pair of functions

Answer 1

Answer:

The value of $(f \circ g)(x)$ is $4+4 x$ and $(g \circ f)(x)$ is $4 x-16$.

Step-by-step explanation:

It is given in the question functions f(x) as 4-x and g(x)=-4x.

It is required to find $(f \circ g)(x)$ and $(g \circ f)(x)$.

To find $(f \circ g)(x)$, substitute g(x)=-4x for x in f(x) and simplify the expression.

To find $(g \circ f)(x)$, substitute f(x)=4-x for x in g(x) and simplify the expression.

Step 1 of 2

Substitute g(x)=-4x for x in f(x) and simplify the expression.

$\begin{aligned}&(f \circ g)(x)=f(g(x)) \\&(f \circ g)(x)=4-g(x) \\&(f \circ g)(x)=4-(-4 x) \\&(f \circ g)(x)=4+4 x\end{aligned}$

Step 2 of 2

Substitute f(x)=4-x for x in g(x) and simplify the expression.

$\begin{aligned}&(g \circ f)(x)=g(f(x)) \\&(g \circ f)(x)=-4 f(x) \\&(g \circ f)(x)=-4(4-x) \\&(g \circ f)(x)=4 x-16\end{aligned}$