Is the function #(x^3+1)/x# odd, even or neither?

1 Answer
Dec 28, 2017

Neither.

Explanation:

Note that:

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

which is the sum of an even function and an odd function, with the result that it is neither.

To confirm, note that:

#f(-1) = ((-1)^3+1)/(-1) = 0#

#f(1) = (1^2+1)/1 = 2#

So #f(-1) != -f(1)# and #f(-1) != f(1)#