Question

is f(x)= x^3-x^2-9x+9 a one to one function

Answer 1

well, let's look at the zeros first
x(x^2-9) - 1(x^2-9) = 0

(x-1)(x-3)(x+3) = 0
so y = 0 for
x = 1 and for x = 3 and for x = -3
that is three values of x for a single value of y, not a good symptom.