SOLUTION: The function f(x)=5x^3-9 is A. Odd B. Even C. Neither How did you know?

Question 200147: The function f(x)=5x^3-9 is
A. Odd
B. Even
C. Neither
How did you know?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Remember, if then the function is an even function. If then the function is an odd function.

First, let's see if is an even function.

Start with the given function.

Replace each x with -x.

Simplify. Note: only the terms with an odd exponent will change in sign.

So this shows us that which means that

Since , this shows us that is not an even function.

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Now, let's see if is an odd function.

Start with the given function.

Negate the entire function by placing a negative outside the function.

Distribute and simplify.

So this shows us that which means that

Since , this shows us that is not an odd function.

--------------------------
Answer:

So the function is neither an even nor odd function.

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