Somnath Jana Asked a Question
October 2, 2020 8:56 ampts 30 pts
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.]
  • 1 Answer(s)
  • 0 Likes
  • 1 Comments
  • Shares
  • Deepak singh thankyou
    see attached proof
    • cropped3772004133288567318.jpg
    Likes(1) Reply(0)
Head Office :
MPA 44, 2nd floor, Rangbari main Road Mahaveer Nagar II, Kota (Raj.) - 324005

Branch Office (Jaipur):
Shyam Tower, Plot No. F2, 6th Floor Amrapali Circle,
Vaishali Nagar, Jaipur, Rajasthan 302021

Mail: info@eduncle.com
All Rights Reserved © Eduncle.com