Question

Let $f\left(x\right)=3x-7$ and $g\left(x\right)=-2x-6$, how do you find $\left(fog\right)\left(4\right)$?

Answer 1

You can solve this in two ways:
(1). plugging the $4$ into $g\left(x\right)$ and then putting what you get from that in to $f\left(x\right)$
(2). plug $g\left(x\right)$ into $f\left(x\right)$ and then plug in the $4$
Option 1:
Plug $4$ into $g\left(x\right)$:
$g\left(x\right)=-2\left(4\right)-6=-8-6=-14$
Then plug $g\left(x\right)$ into $f\left(x\right)$:
$f\left(x\right)=3(-14)-7=-42-7=-49$
Option 2:
Plug $g\left(x\right)$ into $f\left(x\right)$:
$f\left(x\right)=3(-2x-6)-7=-6x-18-7=-6x-25$
Finally plug $4$ into our current $f\left(x\right)$:
$f\left(x\right)=-6\left(4\right)-25=-24-25=-49$.