# If f (x) = 2 + x ; g(x) = x^2 + 5, then what is (f - g)(-5)?

May 4, 2017

$\left(f - g\right) \left(- 5\right) = - 23$

#### Explanation:

If
$\textcolor{w h i t e}{\text{XXX}} \textcolor{g r e e n}{f \left(x\right)} = \textcolor{g r e e n}{2 - x}$
and
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{g \left(x\right)} = \textcolor{b l u e}{{x}^{2} + 5}$
then
$\textcolor{w h i t e}{\text{XXX}} \left(\textcolor{g r e e n}{f} - \textcolor{b l u e}{g}\right) \left(\textcolor{red}{x}\right) = \left(\textcolor{g r e e n}{2 - \textcolor{red}{x}}\right) - \left(\textcolor{b l u e}{{\textcolor{red}{x}}^{2} + 5}\right)$

$\textcolor{w h i t e}{\text{XXXXXXXXX}} = - \left({\textcolor{red}{x}}^{2} + \textcolor{red}{x} + 3\right)$
and
$\textcolor{w h i t e}{\text{XXX}} \left(f - g\right) \left(\textcolor{red}{- 5}\right) = - \left({\textcolor{red}{\left(- 5\right)}}^{2} + \textcolor{red}{\left(- 5\right)} + 3\right)$

$\textcolor{w h i t e}{\text{XXXXXXXXXX}} = - \left(25 - 5 + 3\right)$

$\textcolor{w h i t e}{\text{XXXXXXXXXX}} = - 23$