SOLUTION: Show that the linear function f defined by f (x) = mx + b is an even function if and only if m = 0.

Algebra ->  Functions -> SOLUTION: Show that the linear function f defined by f (x) = mx + b is an even function if and only if m = 0.      Log On


   

Question 943443: Show that the linear function f defined by
f (x) = mx + b is an even function if and only if
m = 0.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) is even when f(-x) = f(x) for all x in the domain.


f(x) = mx + b


f(-x) = m(-x) + b


f(-x) = -mx + b


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Set f(-x) equal to f(x)


f(-x) = f(x)


-mx + b = mx + b


-mx + b-b = mx + b-b ... Subtract b from both sides.


-mx = mx


-mx+mx = mx+mx ... Add mx to both sides.


0 = mx+mx


0 = 2mx


2mx = 0


2mx = 0 means m = 0 (since x is any number, it's not always 0, so m has to be zero)