# How do you find g(f(2)) given g(n)=3n+2 and f(n)=2n^2+5?

May 7, 2017

See a solution process below:

#### Explanation:

First, find $f \left(2\right)$ by substituting every occurrence of $\textcolor{red}{n}$ with $\textcolor{red}{2}$ in the function $f \left(n\right)$ and calculate the result:

$f \left(\textcolor{red}{n}\right) = 2 {\textcolor{red}{n}}^{2} + 5$ becomes:

$f \left(\textcolor{red}{2}\right) = \left(2 \cdot {\textcolor{red}{2}}^{2}\right) + 5$

$f \left(\textcolor{red}{2}\right) = \left(2 \cdot 4\right) + 5$

$f \left(\textcolor{red}{2}\right) = 8 + 5$

$f \left(\textcolor{red}{2}\right) = 13$

Now, we know $g \left(f \left(2\right)\right) = g \left(13\right)$

To find $g \left(13\right)$ substitute every occurrence of $\textcolor{red}{n}$ with $\textcolor{red}{13}$ in the function $g \left(n\right)$ and calculate the result:

$g \left(\textcolor{red}{n}\right) = 3 \textcolor{red}{n} + 2$ becomes:

$g \left(\textcolor{red}{13}\right) = \left(3 \cdot \textcolor{red}{13}\right) + 2$

$g \left(\textcolor{red}{13}\right) = 39 + 2$

$g \left(\textcolor{red}{13}\right) = 41$

$g \left(f \left(2\right)\right) = 41$