# Given f (x) = 4x - 7; g(x) = x +3, what is the value of (g o f) (4)?

Apr 14, 2017

$\left(g \circ f\right) \left(4\right) = \textcolor{m a \ge n t a}{12}$

#### Explanation:

Within this explanation, I will use the notation $g \left(f \left(x\right)\right)$ instead of the given form $\left(g \circ f\right)$; I find it easier to understand.

If $g \left(\textcolor{b l u e}{x}\right) = \textcolor{b l u e}{x} + 3$
and $\textcolor{red}{f \left(x\right)} = \textcolor{red}{4 x - 7}$
then
$\textcolor{w h i t e}{\text{XXX}} g \left(\textcolor{red}{f \left(x\right)}\right) = \textcolor{red}{4 x - 7} + 3$

$\textcolor{w h i t e}{\text{XXXXXXX}} = 4 x - 4$

and if $g \left(f \left(\textcolor{g r e e n}{x}\right)\right) = 4 \textcolor{g r e e n}{x} - 4$
then
$\textcolor{w h i t e}{\text{XXX}} g \left(f \left(\textcolor{g r e e n}{4}\right)\right) = 4 \cdot \textcolor{g r e e n}{4} - 4$

$\textcolor{w h i t e}{\text{XXXXXXX}} = 16 - 4$

$\textcolor{w h i t e}{\text{XXXXXXX}} = 12$