SOLUTION: Tutor Can you help me in determining whether the function is even, odd or neither even or odd? f(x)=x-|x|

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Question 136391: Tutor Can you help me in determining whether the function is even, odd or neither even or odd?
f(x)=x-|x|
Found 2 solutions by solver91311, Nate:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
A function is even if f%28x%29=f%28-x%29 for all x in the domain of f. A function is odd if -f%28x%29=f%28-x%29 for all x in the domain of f. If neither equation holds across the domain, the function is neither even nor odd.

f%28-x%29=-x-abs%28-x%29=-x-abs%28x%29%3C%3Ex-abs%28x%29. Not even.

-f%28x%29=-%28x-abs%28x%29%29=-x%2Babs%28x%29%3C%3E-x-abs%28x%29=f%28-x%29. Not odd.




Note that the graph of the function is not symmetrical about the y-axis which it would be if it were even, nor is it symmetrical about the origin which it would be if it were odd.

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
f(-x) = f(x) is even
f(-x) = -f(x) is odd
~~~~~~~~~
f(x) = x - |x|
f(-x) = -x - |x|
and
-f(x) = -x + |x|
f(-x) does not equal f(x)
f(-x) does not equal -f(x)
Neither~