Question

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

35. f(x) = 3x + 2, g(x) = 5 − 6x

Answer 1

The value of
`$(f \circ g)(x)$` is 17-18x and
`$(g \circ f)(x)$` is -7-18x.

Explanation:

It is given in the question functions f(x) as 3x+2 and g(x)=5-6x.

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

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

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

Step 1 of 2

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

`$$\begin{aligned}&(f \circ g)(x)=f(5-6 x) \\&(f \circ g)(x)=3(5-6 x)+2 \\&(f \circ g)(x)=15-18 x+2 \\&(f \circ g)(x)=17-18 x\end{aligned}$$`

Step 2 of 2

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

`$$\begin{aligned}&(g \circ f)(x)=g(3 x+2) \\&(g \circ f)(x)=5-6(3 x+2) \\&(g \circ f)(x)=5-18 x-12 \\&(g \circ f)(x)=-7-18 x\end{aligned}$$`