# Let f(x) = x + 8 and g(x) = x^2 - 6x - 7 how do you find f(g(2))?

Mar 31, 2017

See the entire solution process below:

#### Explanation:

First, evaluate $g \left(2\right)$ by substituting $\textcolor{red}{2}$ for each occurrence of $\textcolor{red}{x}$ in the function $g \left(x\right)$:

$g \left(\textcolor{red}{x}\right) = {\textcolor{red}{x}}^{2} - 6 \textcolor{red}{x} - 7$ becomes:

$g \left(\textcolor{red}{2}\right) = {\textcolor{red}{2}}^{2} - \left(6 \times \textcolor{red}{2}\right) - 7$

$g \left(\textcolor{red}{2}\right) = 4 - 12 - 7$

$g \left(\textcolor{red}{2}\right) = - 15$

We can now substitute $\textcolor{b l u e}{g \left(2\right)}$ which is $\textcolor{b l u e}{- 15}$ for each occurrence of $\textcolor{b l u e}{x}$ in the function $f \left(x\right)$:

$f \left(\textcolor{b l u e}{x}\right) = \textcolor{b l u e}{x} + 8$ becomes:

$f \left(\textcolor{b l u e}{- 15}\right) = \textcolor{b l u e}{- 15} + 8$

$f \left(\textcolor{b l u e}{- 15}\right) = - 7$

Therefore, $f \left(g \left(2\right)\right) = - 7$