SOLUTION: Find if the function is even, odd or neither. f(x)=x^3+4x

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Question 138649: Find if the function is even, odd or neither.

f(x)=x^3+4x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Remember, if f%28x%29=f%28-x%29 then the function is an even function. If f%28-x%29=-f%28x%29 then the function is an odd function.



First, let's see if f%28x%29=x%5E3%2B4x is an even function.


f%28x%29=x%5E3%2B4x Start with the given function.


f%28-x%29=%28-x%29%5E3%2B4%28-x%29 Replace each x with -x.


f%28-x%29=-x%5E3-4x Simplify. Note: only the terms with an odd exponent will change in sign.



Since f%28x%29%3C%3Ef%28-x%29, this shows us that f%28x%29=x%5E3%2B4x is not an even function.


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Now, let's see if f%28x%29=x%5E3%2B4x is an odd function.

f%28x%29=x%5E3%2B4x Start with the given function.


-f%28x%29=-%28x%5E3%2B4x%29 Negate the entire function by placing a negative outside the function.


-f%28x%29=-x%5E3-4x Distribute and simplify.




Since f(-x)=-f(x), this shows us that f%28x%29=x%5E3%2B4x is an odd function.


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Answer:
So the function f%28x%29=x%5E3%2B4x is an odd function.