SOLUTION: Determine whether g(x)= 2x 3squar - 3x is even, odd, or neither Thanks

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Question 146668: Determine whether g(x)= 2x 3squar - 3x is even, odd, or neither
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Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Is the function g%28x%29=2x%5E3-+3x ??? Get back to me if I'm wrong





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=2x%5E3-3x is an even function.


f%28x%29=2x%5E3-3x Start with the given function.


f%28-x%29=2%28-x%29%5E3-3%28-x%29 Replace each x with -x.


f%28-x%29=-2x%5E3%2B3x Simplify. Note: only the terms with an odd exponent will change in sign.

So this shows us that 2x%5E3-3x%3C%3E-2x%5E3%2B3x which means that f%28x%29%3C%3Ef%28-x%29
Since f%28x%29%3C%3Ef%28-x%29, this shows us that f%28x%29=2x%5E3-3x is not an even function.


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Now, let's see if f%28x%29=2x%5E3-3x is an odd function.

f%28x%29=2x%5E3-3x Start with the given function.


-f%28x%29=-%282x%5E3-3x%29 Negate the entire function by placing a negative outside the function.


-f%28x%29=-2x%5E3%2B3x Distribute and simplify.


So this shows us that -2x%5E3%2B3x=-2x%5E3%2B3x which means that f%28-x%29=-f%28x%29
Since f%28-x%29=-f%28x%29, this shows us that f%28x%29=2x%5E3-3x is an odd function.


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Answer:
So the function f%28x%29=2x%5E3-3x is an odd function.