# If f(x) = ax + b and f(2) = f(4), then what is a?

Jan 4, 2017

$a = 0$ for $f \left(2\right) = f \left(4\right)$

#### Explanation:

First we need to determine what f(2) is and what f(4) is and equate them.

$f \left(2\right) = a 2 + b = 2 a + b$

$f \left(4\right) = a 4 + b = 4 a + b$

We can now equate these two results and solve for $a$

$4 a + b = 2 a + b$

$4 a + b - \textcolor{red}{b} = 2 a + b - \textcolor{red}{b}$

$4 a + 0 = 2 a + 0$

$4 a = 2 a$

$4 a - \textcolor{red}{2 a} = 2 a - \textcolor{red}{2 a}$

$2 a = 0$

$\frac{2 a}{\textcolor{red}{2}} = \frac{0}{\textcolor{red}{2}}$

$a = 0$