1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Given f find g such that g(x)=f(x-1)

  1. Mar 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Find two complex polynomials f and g such that f(0)=f(-1)=1, f(1)=3 and g(x)=f(x-1)

    2. The attempt at a solution
    Using Lagrange polynomial I got f such that f(0)=f(-1)=1, f(1)=3
    Such f is defined by


    Now that I've found f I need to find g such that g(x)=f(x-1), but I don't have any idea of how to do that. Any hint would be appreciated.
    Last edited: Mar 26, 2012
  2. jcsd
  3. Mar 26, 2012 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Given that f(x) = x2+x+1

    Find f(x-1) .
  4. Mar 26, 2012 #3


    User Avatar
    Science Advisor

    You clearly know how to do some fairly complicated Calculus so surely you know how to evaluate a function! Just replace each "x" in [itex]f(x)= x^2+ x+ 12[/itex] with x- 1.
  5. Mar 26, 2012 #4
    Notice that if you define:
    h(x) \equiv f(x) - 1
    then x = 0, and x = -1 are zeros of h. The simplest polynomial that can be written is:
    h(x) = A x (x + 1)
    Then, use the fact that [itex]h(1) = f(1) - 1 = 3 - 1 = 2[/itex] to determine A. You can go back to f trivially then.

    Once you have chosen a particular choice for f, finding g, as explained in the above posts, is fairly trivial (just substitute [itex]x \rightarrow x - 1[/itex], expand and simplify).
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook