determine analytically if the following functions are even o

determine analytically if the following functions are even, odd or neither.

f(x)=2x^3-x

Solution

f(x)=2x^3-x

If f(-x) = f(x) ; function is even

f(-x) = -f(x) ; function is odd

f(-x) = 2(-x)^3 - (-x)

= -2x^3 +x

= - (2x^3 -x)

= -f(x)

Its a odd function