Question

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

34. f(x) = 4 − x, g(x) = −4x

Answer 1

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

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.

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