SOLUTION: my questions are 1.(a)f(x)=2x+5 is neither even nor odd function (b)g(x)=0 is both even and odd

Algebra ->  Rational-functions -> SOLUTION: my questions are 1.(a)f(x)=2x+5 is neither even nor odd function (b)g(x)=0 is both even and odd       Log On


   

Question 995691: my questions are
1.(a)f(x)=2x+5 is neither even nor odd function
(b)g(x)=0 is both even and odd
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
how do you test if the function is odd or even.
here's the test:
http://www.purplemath.com/modules/fcnnot3.htm

if f(x) = f(-x), then the function is even.

if f(-x) = -f(x), then the function is odd.

if neither of these 2 conditions are true, then the function is neither.

f(x) = 2x + 5
f(-x) = -2x + 5
-f(x) = -2x - 5

the function is neither odd nor even because it doesn't pass either test.

g(x) = 0
g(-x) = 0
-g(x) = 0

it passes the test for odd and it passes the test for even and so must be both?

if that's what you're asking, then you are correct in both cases.

i checked online and found several sources referencing the fact that f(x) is both even and odd.

in fact, i believe it is the only function that is both even and odd at the same time.

check the web.

check wikipedia.