SOLUTION: Determine if the function f(x)=x^3|4x| is even, odd, or neither

Question 841946: Determine if the function f(x)=x^3|4x| is even, odd, or neither
Found 2 solutions by jim_thompson5910, richard1234:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
f(x)=x^3|4x|

f(-x)=(-x)^3|4(-x)|

f(-x)=-x^3|4x|

So f(x) does NOT equal f(-x). Therefore, the function is NOT even.

f(x)=x^3|4x|

-f(x)=-x^3|4x|

but we can see that f(-x) = -f(x), so f(x) is indeed an odd function.

Answer: f(x) is an odd function.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
x^3 is odd and |4x| is even.

Odd function * even function = odd function, so f(x) is odd.
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