determining whether this function is one to one or not
how do you determine whether this function is one to one or not?
y = x^3 - 4x^2 + 2
f(a) = f(b), a=/=b
a^3 - 4a^2 +2 = b^3 - 4b^2 +2
a^3 - 4a^2 = b^3 - 4b^2 (subtract 2 from both sides)
a^3 - b^3 - 4a^2 + 4b^2 = 0
(a - b)(a^2 + ab + b^2) - 4(a^2 - b^2) = 0
(a - b)(a^2 + ab + b^2) - 4(a + b)(a - b) = 0
(a - b)(a^2 + ab + b^2 - 4a - 4b) = 0
i'm not sure on what to do next. this is where i'm stuck. what i'm supposed to do is solve for the two factors. for example the first factor results in a = b. but i need to somehow solve for the second factor so i can see whether my two solutions contradict with the statement a=/=b or not. i've been using the above method for all of my homework problems but it doesn't seem to work on this particular problem. my teacher only showed us this way of doing it. any suggestions?