Results 1 to 5 of 5

Math Help - Function analysis

  1. #1
    Member
    Joined
    Oct 2008
    Posts
    131

    Function analysis

    If g(x-1)= x^(2) + 2, then g(x)=?

    Answer = x^(2) + 2x + 3

    Thanks for the help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,539
    Thanks
    779

    Re: Function analysis

    Let's define f(x) = g(x - 1) = x^2 + 2. Then what is f(x + 1)?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,570
    Thanks
    1428

    Re: Function analysis

    Quote Originally Posted by benny92000 View Post
    If g(x-1)= x^(2) + 2, then g(x)=?

    Answer = x^(2) + 2x + 3

    Thanks for the help
    \displaystyle g(x) = g(x - 1 + 1), so if \displaystyle g(x - 1) = x^2 + 2 then \displaystyle g(x) = (x + 1)^2 + 2 = x^2 + 2x + 1 + 2 = x^2 + 2x + 3.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,539
    Thanks
    779

    Re: Function analysis

    Quote Originally Posted by Prove It View Post
    \displaystyle g(x) = g(x - 1 + 1), so if \displaystyle g(x - 1) = x^2 + 2 then \displaystyle g(x) = (x + 1)^2 + 2 = x^2 + 2x + 1 + 2 = x^2 + 2x + 3.
    Strictly speaking, one needs to consider g((x+1)-1): this is the result of substituting x+1 for x in the expression for g(x-1).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,725
    Thanks
    1478

    Re: Function analysis

    Yet another approach: given g(x- 1)= x^2+ 2, let y= x- 1 so that x= y+ 1. Then g(x- 1)= g(y)= (y+ 1)^2+ 2= y^2+ 2y+ 3. And, of course, it follows that g(x)= x^2+ 2x+ 3.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cpx Analysis: Harmonic Function u(z) + ln|z| >= 0
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: September 11th 2010, 01:15 PM
  2. analysis of polynomial function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 3rd 2010, 07:13 AM
  3. Analysis, Dirichlet function
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: April 27th 2010, 03:24 PM
  4. Function analysis
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: October 24th 2009, 06:48 PM
  5. Analysis Function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 13th 2008, 11:23 PM

Search Tags


/mathhelpforum @mathhelpforum