Find inverse functions by solving f(x)=c for simple invertible functions and writing inverse expressions.
Find the inverse of a linear function by swapping x and y and solving
Problem
Find the inverse of the linear function \(f(x)=2x+5\).
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What this problem is really about
An inverse reverses input-output pairs, so the algebra begins by swapping x and y rather than merely rearranging the original rule. We’ll solve the swapped equation for its new output, preserve grouping when dividing, and verify the result by composing the two functions in both orders.
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