Finding the Inverse of f(x) = (2x + 3)/(x - 1)

Algebra 2 · Axiom Academy

EXAMPLE Finding the Inverse of Finding and verifying the inverse of a rational function, step by step. Find the inverse of the rational function , verify the result by composition, and determine the domain and range of both f and f^ -1 . Excellent work — you've found and verified the inverse of a rational function. Remember: The process: replace f(x) with y , swap x and y , solve for y , then replace y with f^ -1 (x) . Algebraic manipulation: multiply to clear the fraction, then collect like terms and factor. Always verify: check that f(f^ -1 (x)) = x to confirm the inverse is correct. Domain and range swap: the domain of f becomes the range of f^ -1 , and the range of f becomes the domain of f^ -1 . Restrictions matter: exclude any value that makes a denominator zero. This method works for any function you can algebraically solve for the inverse of — practice it on other rational functions to make it automatic.

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