# Given f(x) = 2x^3 + x^2 and g(x) = 7x - 2 how do you find (gf)(3)?

May 23, 2018

$g \left(f \left(3\right)\right) = 439$

#### Explanation:

To find $g \left(f \left(3\right)\right)$, we need to find $g \left(f \left(x\right)\right)$ first.

$g \left(x\right)$ is our outside function, so we'll start with that first.

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

Wherever we see an $x$, we'll replace it with $\textcolor{red}{f \left(x\right)}$. We get

g(f(x))=color(blue)(7color(red)((2x^3+x^2))-2

which further simplifies to

$g \left(f \left(x\right)\right) = 14 {x}^{3} + 7 {x}^{2} - 2$

To find $g \left(f \left(3\right)\right)$, we just have to plug $3$ in for $x$. We get

$g \left(f \left(3\right)\right) = 14 {\left(3\right)}^{3} + 7 {\left(3\right)}^{2} - 2$

$\implies = 14 \left(27\right) + 7 \left(9\right) - 2$

$\implies = 378 + 63 - 2$

$\implies 441 - 2$

$g \left(f \left(3\right)\right) = 439$

Hope this helps!