Question

Is f(x) = x^3 - x even, odd, or neither. Explain your answer.

Answer 1

odd

Explanation:

a function is even when f(-x) =f(x) and a function is odd

when f(-x)= -f(x)

so let's substitute -x into our function

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

= -x^3 +1

so, f(-X)= -f(x)

therefore our function is odd

Answer 2

Odd function : f(-x) = -f(x)
Even function : f(-x) = f(x)

f(-x) = (-x)^3 = -x^3 = -f(x) thus it’s an odd function