Proof: If x1 != x2, then f(x1) != f(x2).

[Jamers328]

This is for my Intro to Advanced Math class. By !=, I mean 'not equal to'.

We have to prove: If x1 != x2, then f(x1) != f(x2) by the contrapositive.

f(x)=3x-5

I found the contrapositive: If f(x1) = f(x2), then x1 = x2.

I don't know how to start the proof. I'm sure if someone can just give me the first line, I can do it, because it's easy enough and I understand the concept completely.

Thanks a lot!

 

[pka]

\(\displaystyle f(x) = 3x - 5\)
\(\displaystyle f(a) = f(b)\quad \Rightarrow \quad 3a - 5 = 3b - 5\)
Prove that \(\displaystyle a=b\)

 

[Jamers328]

Thanks pka, easy enough. You are always so good to me.