Question

f(x) = 3x - 7 and g(x) = -2x -6Find (f o g)(4) (see image)I need to understand the step by step steps for how to solve this problem

Answer 1

$\begin{gathered} f(x)=3x-7 \\ g(x)=-2x-6 \end{gathered}$

Composition of functions:

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

1. Find (fog)(x): Substitute the imputs (x-values) in f for function g:

$(f\circ g)(x)=3(-2x-6)-7$

2. Simplify:

$\begin{gathered} (f\circ g)(x)=-6x-18-7 \\ (f\circ g)(x)=-6x-25 \end{gathered}$

3. Find (fog)(4). Evaluate the fucntion (fog) when x=4:

$\begin{gathered} (f\circ g)(4)=-6(4)-25 \\ (f\circ g)(4)=-24-25 \\ (f\circ g)(4)=-49 \end{gathered}$Then, (fog)(4) is:$(f\circ g)(4)=-49$