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    NationalMediumFunctions10–12

    Inverse of a Rational Function

    Inversa de uma Função Racional

    Let f(x)=3x−1x+2f(x) = \frac{3x - 1}{x + 2}, defined for x≠−2x \neq -2. Find an expression for f−1(x)f^{-1}(x) and state its domain.

    Set yy equal to the expression and solve for xx: collect every term containing xx on one side before factoring it out. The domain of the inverse comes from the new denominator.

    Solution

    Step 1 of 7

    1. 1.Put y=3x−1x+2y = \frac{3x - 1}{x + 2} and clear the denominator: