how do you prove that this is a one to one function algebraically?(adsbygoogle = window.adsbygoogle || []).push({});

y = x^3 - 4x^2 + 2

this is what i've done so far:

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 have no idea what to do after this. i know there are probably easier ways of determining whether a function is one to one or not but my teacher wants us to do it this way.

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# Homework Help: How do u prove that this is a one to one function

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