Determine algebraically whether the function is even, odd, or neither.

Question

Determine algebraically whether the function is even, odd, or neither. (show all work for full credit!)

 

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

Answer 1

A function is even if f(-x) = f(x).  A function is odd if f(-x) = -f(x).

 

f(x) = x³ / (x²+1)

 

f(-x) = (-x)³ / ( (-x)²+1) = -x³ / (x²+1)

 

                                     = -f(x)

 

So, the given function is an ODD function.