Find inverse functions for simple invertible functions, including rational examples.
Find an inverse function by swapping x and y and solving a linear equation
Problem
Find \(f^{-1}(x)\) for \(f(x)~=~3x~-~5\).
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What this problem is really about
An inverse reverses the roles of input and output, so begin by writing the rule with y and swapping the variables. Then solve for the new output by undoing the original operations in reverse order. A composition check is the cleanest way to catch a sign or operation-order error: the two functions should return the starting input.
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