If R->R, where f (x)=7x +5

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

Therefore 7a+5 = 7b+5

Therefore 7a=7b

Therefore a=b

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

Therefore 7x+5= y

Therefore x=y+5/ 7

Therefore x= an element of R

Is this working (minus the incorrect symbols) correct?

Thanks for the help