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    IBMediumFunctions10–12

    Inverse of a Rational Function and Its Domain

    Inversa de uma Função Racional e o Seu Domínio

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

    Set y equal to the expression and rearrange until every x is on one side. The excluded value of the inverse is not guessed at the end — it comes from the step where you divide by a bracket.

    Solution

    Step 1 of 9

    1. 1.Write y = \frac{2x + 3}{x - 1} and clear the fraction: