Question

The function f(x) = x 2 is an even function.
True
False

Answer 1

to test a function as odd or even substitute -x for x

i.e f(-x) if f(-x) = f(x) the function is even
f(-x) = -f(x) the function is odd


the 3rd case is neither

e.g f(x) = x^4 -3 f(-x) = (-x)^4 - 3= x^4 - 3 = f(x) so even

f(x) = x^3 - x (f(-x) = (-x)^3 -(-x) = -x^3 + x = -1(x^3 - x) - -f(x) odd

f(x) = x^6 - x f(-x) = (-x)^6 - (-x) = x^6 + x (neither)