# Math Help - Injective Function

1. ## Injective Function

Let f: R-{-2} -> R defined by f(x)=(2x-1)/(x+2)

Prove that f is injective. Thank you.

2. In this kind of question you first set $f(a) = f(b)$
Here it gives $\frac{2a-1}{a+2} =\frac{2b-1}{b+2}$.
And you juggle with a and b to show that $f(a) = f(b)$ implies a=b.

$(2a-1)(b+2) =(2b-1)(a+2)$

$2ab+4a-b-2 =2ab+4b-a-2$à

$4a-b=4b-a$

$5a=5b$

$a=b$