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# for #f(2) = f(4)#

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

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

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

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

#4a + b = 2a + b#

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

#4a + 0 = 2a + 0#

#4a = 2a#

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

#2a = 0#

#(2a)/color(red)(2) = 0/color(red)(2)#

#a = 0#