SOLUTION: Determine algebraically whether f(x) = |x^3-x|+3cos(x) is even, odd, or neither. And i need to know how you got the answer, thanks.

Algebra ->  Rational-functions -> SOLUTION: Determine algebraically whether f(x) = |x^3-x|+3cos(x) is even, odd, or neither. And i need to know how you got the answer, thanks.      Log On


   

Question 336017: Determine algebraically whether f(x) = |x^3-x|+3cos(x) is even, odd, or neither. And i need to know how you got the answer, thanks.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=abs%28x%5E3-x%29%2B3cos%28x%29
f%28-x%29=abs%28%28-x%5E3%29-%28-x%29%29%2B3cos%28-x%29
From trigonometry,
cos%28x%29=cos%28-x%29
f%28-x%29=abs%28-x%5E3%2Bx%29%2B3cos%28x%29
f%28-x%29=abs%28%28-1%29%28x%5E3-x%29%29%2B3cos%28x%29
f%28-x%29=abs%28x%5E3-x%29%2B3cos%28x%29
f%28-x%29=f%28x%29
So the function is even.