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Thread: [SOLVED] Function Question

  1. #1
    Member looi76's Avatar
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    [SOLVED] Function Question

    Question:
    The functions f and g are defined by:
    $\displaystyle f : x \mapsto 3x + 2$███$\displaystyle x \in \Re$

    $\displaystyle g : x \mapsto \frac{6}{2x + 3}$███$\displaystyle x \neq 1.5$

    (i)...
    (ii)...
    (iii) Express each of $\displaystyle f^{-1}(x)$ and $\displaystyle g^{-1}(x)$ in terms of $\displaystyle x$, and solve the equation $\displaystyle f^{-1}(x) = g^{-1}(x)$


    Attempt:

    $\displaystyle f(x) = 3x + 2$
    $\displaystyle y = 3x + 2$
    $\displaystyle y - 2 = 3x$
    $\displaystyle \frac{y - 2}{3} = x$

    $\displaystyle f^{-1}(x) = \frac{x - 2}{3}$

    $\displaystyle g(x) = \frac{6}{2x + 3}$

    I don't know how to get the inverse of g(x)
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi

    The same idea should work :

    $\displaystyle y=\frac{6}{2x+3}$

    You want an equality starting by $\displaystyle x=\ldots$ so multiply both sides by $\displaystyle 2x+3$ and then bring $\displaystyle y$ to the right hand side.
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