SOLUTION: Is f(x) = x^5 x an even or odd or neither odd nor even function? This is my attemp. F(-x) =(-x)^5 -x=-(x^5 x)

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Question 696573: Is f(x) = x^5 x an even or odd or neither odd nor even function? This is my attemp. F(-x) =(-x)^5 -x=-(x^5 x)
Found 2 solutions by Edwin McCravy, josmiceli:
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
The rules are:

1. Substitute (-x) for x in the equation
2. Simplify
3. (a) If the right side is exactly the same as the 
original right side, then its graph is symmetrical
with respect to the y-axis.
   (b) If the right side is like the original except 
that it is multiplied by -1, then it is an odd function,
and is reflected in the origin.
   (c) If neither (a) or (b) apply then it is neither
an even function or an odd function.


     f(x) = x5 

1.  f(-x) = (-x)5

2.  f(-x) = -x5 

That's the right side of the original multiplied
through by -1.  Therefore it's odd.  

Edwin
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
It's not even, because replacing (x) with (-x) does
not give the same value of f(x), which is a reflection
about the vertical axis.
---------------------
It is an odd function because replacing (x) with (-x)
changes the sin of f(x)


-----------------
and, likewise
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