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Math Help - Find a function

  1. #1
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    Find a function

    Find a function f(x)=x^kand a function g such that f(g(x))=h(x)=\sqrt{3x+x^2}.
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  2. #2
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    Quote Originally Posted by Zeppelin View Post
    Find a function f(x)=x^kand a function g such that 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 g(x), such that if f(x)=x^k then:

    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.

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

    so taking k-th roots:

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

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

    RonL
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