# Let f(x) = 9x - 2 and g(x) = -x + 3, how do you find f(g(x))?

Feb 15, 2017

$f \left(g \left(x\right)\right) = - 9 x + 25$

#### Explanation:

Substitute x = - x + 3, that is g(x) into f(x)

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

$\textcolor{w h i t e}{f \left(g \left(x\right)\right)} = 9 \left(\textcolor{red}{- x + 3}\right) - 2$

$\textcolor{w h i t e}{f \left(g \left(x\right)\right)} = - 9 x + 27 - 2$

$\textcolor{w h i t e}{f \left(g \left(x\right)\right)} = - 9 x + 25$