Let f: R-{-2} -> R defined by f(x)=(2x-1)/(x+2)
Prove that f is injective. Thank you.
In this kind of question you first set $\displaystyle f(a) = f(b) $
Here it gives $\displaystyle \frac{2a-1}{a+2} =\frac{2b-1}{b+2}$.
And you juggle with a and b to show that $\displaystyle f(a) = f(b) $ implies a=b.
$\displaystyle (2a-1)(b+2) =(2b-1)(a+2)$
$\displaystyle 2ab+4a-b-2 =2ab+4b-a-2$à
$\displaystyle 4a-b=4b-a$
$\displaystyle 5a=5b$
$\displaystyle a=b$