SOLUTION: Determine if the function is even, odd, or neither. f(x) = -4x3 + 7x please explain in detail how to solve this I really want to understand it thank you.

Algebra ->  Functions -> SOLUTION: Determine if the function is even, odd, or neither. f(x) = -4x3 + 7x please explain in detail how to solve this I really want to understand it thank you.      Log On


   

Question 1071547: Determine if the function is even, odd, or neither.
f(x) = -4x3 + 7x
please explain in detail how to solve this I really want to understand it thank you.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Even functions have the property f(-x) = f(x) over all x in the domain of f.
Odd functions have the property f(-x) = -f(x) over all x in the domain of f.
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+f%28x%29=x%5E2+ is an example of an even function because f(-x) = f(x)
Try it: +f%28-4%29+=+%28-4%29%5E2+=+16+=+%284%29%5E2+=+f%284%29+
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++f%28x%29=x%5E3+ is an example of an odd function because f(-x) = -f(x)
Try it: +f%28-2%29+=+%28-2%29%5E3+=+-8+=+-%282%5E3%29=+-f%282%29+
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On to the problem at hand: +f%28x%29=-4x%5E3+%2B+7x+
Let's look at f(-x) and see how that relates to f(x):
+f%28-x%29+=+-4%28-x%5E3%29+%2B+7%28-x%29+
= +-4%28-1%5E3%29%28x%5E3%29+-+7x+
= ++4x%5E3+-+7x+
= +-%28-4x%5E3+%2B+7x%29+
The part in the parenthesis is nothing more than f(x):
= ++-f%28x%29+
Since f(-x) = -f(x) this function is an odd function.
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Ans: +f%28x%29+=+-4x%5E3+%2B+7x+ is an ODD function.
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