# Question #de8d3

May 28, 2017

$- 40 x + 31$

#### Explanation:

First, let's understand what $f \left(x\right)$ means:

$f \left(x\right)$ is a function that takes whatever is put inside the parentheses and does something to it. Some examples are:

$\textcolor{w h i t e}{\text{XXX}} f \left(\textcolor{red}{3}\right) = - 4 \left(\textcolor{red}{3}\right) + 7$
$\textcolor{w h i t e}{\text{X}} f \left(\textcolor{b l u e}{1200}\right) = - 4 \left(\textcolor{b l u e}{1200}\right) + 7$
$\textcolor{w h i t e}{\text{XXX}} f \left(\textcolor{b r o w n}{y}\right) = - 4 \left(\textcolor{b r o w n}{y}\right) + 7$
$f \left(\textcolor{\lim e g r e e n}{{x}^{2} - 8}\right) = - 4 \left(\textcolor{\lim e g r e e n}{{x}^{2} - 8}\right) + 7$

So, to evaluate $f \left(\textcolor{\mathmr{and} a n \ge}{g \left(x\right)}\right)$, just plug $\textcolor{\mathmr{and} a n \ge}{g \left(x\right)}$ into $f \left(x\right)$.

$f \left(\textcolor{\mathmr{and} a n \ge}{g \left(x\right)}\right) = - 4 \left(\textcolor{\mathmr{and} a n \ge}{g \left(x\right)}\right) + 7$

$\textcolor{w h i t e}{\text{XXX..-}} = - 4 \left(\textcolor{\mathmr{and} a n \ge}{10 x - 6}\right) + 7$

Now simplify.

$\textcolor{w h i t e}{\text{.-....}} - 4 \left(10 x - 6\right) + 7$

$= - 40 x - 4 \left(- 6\right) + 7$

$= - 40 x + 24 + 7$

$= - 40 x + 31$