# How do you find (gof)(x) given f(x)=-3x+7 and g(x)=x^2-8?

May 20, 2017

$\left(g \circ f\right) \left(x\right) = 9 {x}^{2} - 42 x + 41$

#### Explanation:

To make it a bit more obvious what is happening:

Set $f \left(x\right) = z = - 3 x + 7$

$g \left(z\right) = {z}^{2} - 8$

So by substitution:

$\left(g \circ f\right) \left(x\right) \to g \left(z\right) = {\left(- 3 x + 7\right)}^{2} - 8$

$\left(g \circ f\right) \left(x\right) = 9 {x}^{2} - 42 x + 49 - 8$

$\left(g \circ f\right) \left(x\right) = 9 {x}^{2} - 42 x + 41$

Aug 5, 2018

$g \left(f \left(x\right)\right) = {\left(- 3 x + 7\right)}^{2} - 8$

#### Explanation:

We have the composite function $g \left(f \left(x\right)\right)$. Notice that $f \left(x\right)$ is the inside function, so we can plug this into $g \left(x\right)$. We get

$\textcolor{s t e e l b l u e}{f \left(x\right) = - 3 x + 7}$

$\textcolor{p u r p \le}{g \left(x\right) = {x}^{2} - 8}$

color(purple)(g(color(steelblue)(f(x)))=(color(steelblue)(-3x+7))^2-8

Hope this helps!