Results 1 to 2 of 2

Thread: Find a function

  1. #1
    Newbie
    Joined
    Aug 2006
    Posts
    9

    Find a function

    Find a function $\displaystyle f(x)=x^k$and a function $\displaystyle g$ such that $\displaystyle f(g(x))=h(x)=\sqrt{3x+x^2}$.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    5
    Quote Originally Posted by Zeppelin View Post
    Find a function $\displaystyle f(x)=x^k$and a function $\displaystyle g$ such that $\displaystyle f(g(x))=h(x)=\sqrt{3x+x^2}$.
    The wording here is a bit confused, but I will assume that we seek a function $\displaystyle g(x)$, such that if $\displaystyle f(x)=x^k$ then:

    $\displaystyle f(g(x))=h(x)=\sqrt{3x+x^2}$

    For the moment I will not worry about the domain/s of the functions but go through a formal manipulation of the expressions and then worry about the domains later.

    $\displaystyle f(g(x))=(g(x))^k=\sqrt{3x+x^2}=(3x+x^2)^{1/2}$,

    so taking k-th roots:

    $\displaystyle g(x)=(3x+x^2)^{1/2k}$,

    and the domain of $\displaystyle g$ and $\displaystyle h$ is $\displaystyle \{x: x \in \mathbb{R}, \mbox{ and }x \le -3,\ \mbox{ or } x \ge 0\}$

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] How to find the function v=f(t,k) for which dv/dt = k/v
    Posted in the Calculus Forum
    Replies: 6
    Last Post: Apr 16th 2011, 09:26 AM
  2. Replies: 14
    Last Post: Jan 18th 2010, 06:16 PM
  3. Find a Function G and F[x]
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Oct 13th 2007, 08:51 PM
  4. Replies: 3
    Last Post: Jul 17th 2007, 11:06 AM
  5. How do I find the function of x
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Nov 27th 2005, 09:22 AM

Search Tags


/mathhelpforum @mathhelpforum