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

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Answer 1 · 2017-01-04T19:33:26

$a = 0$ $a = 0$ for $f (2) = f (4)$ $f(2) = f(4)$

First we need to determine what $f (2) i s and w ˆ$ $f(2) is and what$ f(4) is and equate them.

$f (2) = a 2 + b = 2 a + b$ $f(2) = a2 + b = 2a + b$

$f (4) = a 4 + b = 4 a + b$ $f(4) = a4 + b = 4a + b$

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

$4 a + b = 2 a + b$ $4a + b = 2a + b$

$4 a + b - b = 2 a + b - b$ $4a + b - color(red)(b) = 2a + b - color(red)(b)$

$4 a + 0 = 2 a + 0$ $4a + 0 = 2a + 0$

$4 a = 2 a$ $4a = 2a$

$4 a - 2 a = 2 a - 2 a$ $4a - color(red)(2a) = 2a- color(red)(2a)$

$2 a = 0$ $2a = 0$

$\frac{2 a}{2} = \frac{0}{2}$ $(2a)/color(red)(2) = 0/color(red)(2)$

$a = 0$ $a = 0$