Can someone please explain to me- because I feel I got this wrong:

f: Z → Z , where f(x) = x -10;

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

therefore Xa-10=Xb-10

therefore -10a=-10b

therefore -a=-b

is this the wrong way? functions are still confusing me

any help would be much appreciated