can anyone explain me how to calculate surjectivity and injectivity of a function on a following example
f(x) = -x^2 + 3
I know that the function is infective if f(x1) = F(x2) = -x^2+3 = -x^2+3 so -x^2 = -x^2 (hope that's correct)
and if I take f(3) = -6 and f(-3) = -6
so the function is not injective
for surjectivity y = -x^2+3 but I don't know why it is NOT surjective...
Is there any simpler way to go through this. I don't know how I should show the answers on the exam...