Results 1 to 2 of 2

Math Help - Proof?(functions)

  1. #1
    Super Member fardeen_gen's Avatar
    Joined
    Jun 2008
    Posts
    539

    Proof?(functions)

    Consider a real valued function f(x) satisfying, 2f(xy) = (f(x))^y + (f(y))^x for all real x\ \mbox{\&}\ y and f(1) = a where a\neq 1. Prove that (a - 1)\sum_{i = 1}^{n}f(i) = a^{n + 1} - a.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,386
    Thanks
    1323
    Quote Originally Posted by fardeen_gen View Post
    Consider a real valued function f(x) satisfying, 2f(xy) = (f(x))^y + (f(y))^x for all real x\ \mbox{\&}\ y and f(1) = a where a\neq 1. Prove that (a - 1)\sum_{i = 1}^{n}f(i) = a^{n + 1} - a.
    Taking y= 1, 2f(x)= f(x)+ f(1)^x= f(x)+ a^x. That is, f(x)= a^x. That should be all you need.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proof regarding 1-1 functions
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 15th 2009, 03:54 PM
  2. Proof using functions
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 15th 2009, 12:25 PM
  3. functions proof (is it right?)
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 10th 2009, 01:56 PM
  4. Functions Proof
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: March 1st 2009, 05:42 PM
  5. Proof regarding functions
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: January 13th 2009, 08:42 PM

Search Tags


/mathhelpforum @mathhelpforum