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

Jan 25, 2016

$f \left(g \left(x\right)\right) = 4 {x}^{2} + 9$

#### Explanation:

$f \left(x\right) = 2 x - 5$

$g \left(x\right) = 2 {x}^{2} + 7$

To find $f \left(g \left(x\right)\right)$, what you need to do is plug $g \left(x\right)$ for each occurence of $x$ in $f \left(x\right)$:

$f \left(\textcolor{b l u e}{x}\right) = 2 \textcolor{b l u e}{x} - 5$

$f \left(g \left(x\right)\right) = f \left(\textcolor{b l u e}{2 {x}^{2} + 7}\right) = 2 \left(\textcolor{b l u e}{2 {x}^{2} + 7}\right) - 5$

$= 4 {x}^{2} + 14 - 5 = 4 {x}^{2} + 9$