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

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) (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

-------------------------------------------------------

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)
RELATED QUESTIONS
show that if f is any function thaen the function 0 defined by 0(x)=f(x)-f(-x)/2 is... (answered by robertb)

A function f is called even if f(-x)=f(x) and it is called odd if f(-x)=-f(x). Show that (answered by venugopalramana)

True or false: if f is an odd function whose domain is the set of real numbers and a... (answered by Fombitz)

Suppose f is the function whose domain is the interval [−2, 2], with f defined by... (answered by richard1234)

If f(x) is a linear function such that f(0)=48 and f(2)=0, identify the slope m of the... (answered by Edwin McCravy)

If f is a linear function, f(0.1) = 9.3, and f(0.4) = −6.3, find an equation f(x)... (answered by CubeyThePenguin)

The one to one function f is defined on the domain x>0 by f(x) = (2x-1)/(x+2). A) State... (answered by josgarithmetic)

Which function is defined by f(x)=b^x, where b>0,b≠ 1, and the exponent x is any... (answered by josgarithmetic)

Part I. G(x) = -x4 + 32x2 +144 a. Show whether G is an even, odd function or... (answered by MathLover1)