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

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


   

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) 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=5x%5E3-9 is an even function.


f%28x%29=5x%5E3-9 Start with the given function.


f%28-x%29=5%28-x%29%5E3-9 Replace each x with -x.


f%28-x%29=-5x%5E3-9 Simplify. Note: only the terms with an odd exponent will change in sign.

So this shows us that 5x%5E3-9%3C%3E-5x%5E3-9 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=5x%5E3-9 is not an even function.


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Now, let's see if f%28x%29=5x%5E3-9 is an odd function.

f%28x%29=5x%5E3-9 Start with the given function.


-f%28x%29=-%285x%5E3-9%29 Negate the entire function by placing a negative outside the function.


-f%28x%29=-5x%5E3%2B9 Distribute and simplify.


So this shows us that -5x%5E3-9%3C%3E-5x%5E3%2B9 which means that f%28-x%29%3C%3E-f%28x%29

Since f%28-x%29%3C%3E-f%28x%29, this shows us that f%28x%29=5x%5E3-9 is not an odd function.



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Answer:

So the function f%28x%29=5x%5E3-9 is neither an even nor odd function.