Results 1 to 3 of 3
Like Tree1Thanks
  • 1 Post By Plato

Math Help - Composite Functions

  1. #1
    Newbie
    Joined
    Dec 2012
    From
    Wisconsin
    Posts
    2

    Composite Functions

    Hello, just discovered this site and it looks to be very helpful! I have two questions regarding my Pre-Calc homework:

    1. First Question:A function f is given which satisfies f(1/(x+1))= 2x-12 for all real numbers x. Compute f(1) and f(f(2)). What are the range and domain of f?

    My understanding is that I can treat (1/(x+1)) like a g(x) and so for f(1), I would insert 1 and come up with f(1/2). Then I would plug in 1/2 into 2x+12 to get 1+12=13, so f(1)=13. Am I following these steps properly? Then for f(f(2)), would I insert a 2 into the input, calculate the output and then use that output as the next input to the same equation?

    2. Second Question: Does there exist a function f which satisfies f(x^2)=x+1 for all real numbers x? I believe this function would just be f(x)=x^2+1 which I get by substituting x^2 into the output, but want to make sure there isn't something I am missing.

    Any help would be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,616
    Thanks
    1579
    Awards
    1

    Re: Composite Functions

    Quote Originally Posted by leolson3 View Post
    Hello, just discovered this site and it looks to be very helpful! I have two questions regarding my Pre-Calc homework:
    1. First Question:[I]A function f is given which satisfies f(1/(x+1))= 2x-12 for all real numbers x. Compute f(1) and f(f(2)). What are the range and domain of f?

    Look at it this way: if \frac{1}{a+1}=1 then a=~?

    Once you have that, what is 2a-12=~?
    Thanks from leolson3
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Dec 2012
    From
    Wisconsin
    Posts
    2

    Re: Composite Functions

    Just realized I had a typo, above, it should indeed be 2x-12 as I initially put.

    So a would equal 0 and f(1) would be -12?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help with composite functions
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 14th 2012, 07:06 PM
  2. composite functions
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: October 10th 2009, 05:09 AM
  3. Composite Functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 5th 2009, 02:19 PM
  4. Composite Functions
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: August 22nd 2009, 06:25 PM
  5. Composite functions
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: July 25th 2007, 10:06 PM

Search Tags


/mathhelpforum @mathhelpforum