SOLUTION: Determine algebraically if each function is even, odd, or neither. A. f(x) = (2x^2 + 1)^(1/3) B. 2x/|x|

Algebra ->  Equations -> SOLUTION: Determine algebraically if each function is even, odd, or neither. A. f(x) = (2x^2 + 1)^(1/3) B. 2x/|x|       Log On


   

Question 1208042: Determine algebraically if each function is even, odd, or neither.

A. f(x) = (2x^2 + 1)^(1/3)

B. 2x/|x|


Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.

(A)  In the formula for function  f(x) = (2x^2 + 1)^(1/3)  replace  x  by  -x.


     You will see that the value f(-x) is the same as the value of f(x).


     It means that this function f(x) is even.




(B)  In the formula for function  g(x) = %282x%29%2Fabs%28x%29  replace  x  by  -x.


     You will see that the value g(-x) is of opposite sign comparing with g(x).


     It means that this function g(x) is odd.



     By the way, the formula for g(x), after canceling/reducing is

          g(x)= 1  for  x > 0,   g(x) = -1  for x < 0,   which also points that g(x) is an odd function.

Solved.