The function is not a bijection because two different values of x
map to a single value of f(x). Each value of f(x) must map to a unique value of x and vice versa. For example, x = 1 and -1 both map to f(x)=2.
f(x)=3-x^2 is surjective (onto) because for each value of f(x) there's at least one value of x.
This can be seen in the continuity of the parabolic curve.