Show that f (x) = (x-2) ^3+8 is one to one algebraically

What im thinking is this: F (a) = f (b) so have 2 equations written and plug a into one and b in the other

(a-2) ^3+8 = a^3-8+8 = a^3

= a^3 = b^3 square root both side = a=b

(b-2) ^3+8 = b^3-8+8 = b^3

Thus it is 1:1.