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Homework Statement
[tex]y=(x+1)^3[/tex]
Homework Equations
f(a)=f(b)
a=b
The Attempt at a Solution
[tex](a+1)^3 =(b+1)^3[/tex]
[tex]1+3 a+3a^2+a^3=1+3b+3b^2+b^3[/tex]
This is where I get stuck.
I know what the difference of cubes is but I can't seem to figure out how to apply that to this case. I was under the impression that if I was to apply the difference of cubes that the equation would gabber to be in, the form [tex](x^3)+1[/tex] rather than [tex](x+1)^3[/tex] I'm probably forgetting something here :PHow about: if [itex](a+1)^3 =(b+1)^3\,,[/itex] then [itex](a+1)^3-(b+1)^3=0\,.[/itex]
Then factor into difference of cubes.
I haven't taken calculus yet but would it suggestion look like this? f(x)=(x+1)^3 I've already graphed it & seen that it's 1:1 but I'm looking to do this algebraically. Excuse me if I misinterpreted your post.Do you know any calculus? That's the easy way to prove this. Show y is an always increasing function of x.