- #1
demonelite123
- 219
- 0
how do you prove that this is a one to one function algebraically?
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.
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.