Question

true or false
The function f is an odd function if f(-x) = -f(x).

Answer 1

true e.g f(x) = x^3 f(-x) = (-x)^3 so f(-x) = -x^3 or f(-x) = - f(x)

even function f(-x) = f(x)

e.g f(x) = x^2 f(-x) = (-x)^2 = x^2 fo f(-x) = f(x)

and there is also the case where the function is neither odd nor even

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

neither odd nor even