# Given f(x) = x^2 - 4 and g(x) = 2x - 1 , how do you determine the value of (f + g)(3)?

Apr 14, 2017

See the entire solution process below:

#### Explanation:

$\left(f + g\right) \left(x\right) = f \left(x\right) + g \left(x\right) = \left({x}^{2} - 4\right) + \left(2 x - 1\right)$

Therefore:

$\left(f + g\right) \left(x\right) = \left({x}^{2} - 4\right) + \left(2 x - 1\right)$

To find $\left(f + g\right) \left(3\right)$ we must substitute $\textcolor{red}{3}$ for every occurrence of $\textcolor{red}{x}$ in $\left(f + g\right) \left(x\right)$:

$\left(f + g\right) \left(\textcolor{red}{x}\right) = \left({\textcolor{red}{x}}^{2} - 4\right) + \left(2 \textcolor{red}{x} - 1\right)$ becomes:

$\left(f + g\right) \left(\textcolor{red}{3}\right) = \left({\textcolor{red}{3}}^{2} - 4\right) + \left(\left(2 \cdot \textcolor{red}{3}\right) - 1\right)$

$\left(f + g\right) \left(\textcolor{red}{3}\right) = \left(9 - 4\right) + \left(6 - 1\right)$

$\left(f + g\right) \left(\textcolor{red}{3}\right) = 5 + 5$

$\left(f + g\right) \left(\textcolor{red}{3}\right) = 10$