# Given f(x) = 4x + 5 and g(x) = 7x - 2 how do you find (f - g)(7)?

Sep 25, 2017

See a solution process below:

#### Explanation:

First, let's find $\left(f - g\right) \left(x\right)$:

$\left(f - g\right) \left(x\right) = f \left(x\right) - g \left(x\right) = \left(4 x + 5\right) - \left(7 x - 2\right)$

$\left(f - g\right) \left(x\right) = 4 x + 5 - 7 x + 2$

$\left(f - g\right) \left(x\right) = 4 x - 7 x + 5 + 2$

$\left(f - g\right) \left(x\right) = \left(4 - 7\right) x + \left(5 + 2\right)$

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

To find $\left(f - g\right) \left(7\right)$ substitute $\textcolor{red}{7}$ for each occurrence of $\textcolor{red}{x}$ in $\left(f - g\right) \left(x\right)$:

$\left(f - g\right) \left(\textcolor{red}{x}\right) = - 3 \textcolor{red}{x} + 7$ becomes:

$\left(f - g\right) \left(\textcolor{red}{7}\right) = \left(- 3 \cdot \textcolor{red}{7}\right) + 7$

$\left(f - g\right) \left(\textcolor{red}{7}\right) = - 21 + 7$

$\left(f - g\right) \left(\textcolor{red}{7}\right) = - 14$