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Thread: combining functions

  1. #1
    Newbie allywallyrus's Avatar
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    combining functions

    $\displaystyle f(x)=3^x$ $\displaystyle g(x)=x+2$ $\displaystyle h(x)=2x-3$ which i need to arrange to get $\displaystyle y=\frac{1}{27}*3^{2x}+2$
    i can get the last part of the equation when i do $\displaystyle g*f(x+3)*h(x)$ but not sure where the fraction comes from
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  2. #2
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    Quote Originally Posted by allywallyrus View Post
    $\displaystyle f(x)=3^x$ $\displaystyle g(x)=x+2$ $\displaystyle h(x)=2x-3$ which i need to arrange to get $\displaystyle y=\frac{1}{27}*3^{2x}+2$
    i can get the last part of the equation when i do $\displaystyle g*f(x+3)*h(x)$ but not sure where the fraction comes from
    Hi

    $\displaystyle 3^{2x-3} = \frac{3^{2x}}{3^3} = \frac{3^{2x}}{27}$
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  3. #3
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    Just note that $\displaystyle 3^{-3}=\frac{1}{27}$ and $\displaystyle f \circ g(x) = 3^{2x - 3} $.
    You finish in one more step.
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  4. #4
    Newbie allywallyrus's Avatar
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    oh wow i hadnt even thought of that
    thanks
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