7. a function f: r> r is continuous on r and f(t = )+f) for all , y €r. prove that f(z) = ax +b, (a, b e r) for all c e r. hint. flr) = lf(2r) +f(0)], f (r) +f(

7. A function f: R> R is continuous on R and f(t = )+f) for all , y €R. Prove that f(z) = ax +b, (a, b E R) for all c E R. Hint. flr) = lf(2r) +f(0)], f (r) +f(u) = (2r) +f(2y)]+f(0) = fz+y) +f(0). Let o(T) = f(r) - f(0). Then o is continuous on R and o(r + y) = o(r) ++ o(y). Worked Ex.5, page 253.]