Is this the correct approach?

If not, a breakdown of the steps needed would be greatly appreciated

I need to prove if the following function is a bijection or is not a bijection

f: R-->R, where f(x)= -2x+1

let a,b be an element of R and let f(a)=f(b)

therefore -2a+1=-2b+1

therefore -2a=-2b

therefore a=b

therefore a=b

let y be an element of R and let f(x)=y

therefore -2x+1=y

therefore x= y-1/-2

therefore x= element of R

Guessing this is wrong....