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Jul 30, 2021 · Verifying inverse functions from tables. Worked example: Continuity at a point (graphical) Worked example: point where a function is continuous. Worked example: point where a function isn't continuous. Worked example: using the intermediate value theorem. Working with matrices as transformations of the plane

Yes, f(x) = 2x/(x^2-1) is not invertible. But restricting it's domain to (-1,1) would allow us to conclude that the inverse of the function f is 1/y.(1 - sqrt(1+x^2)) and the graph of the same is as below. Now, f-inverse(x) = 1/x.[1-sqrt(x^2+1)] and f(x) = 2x/(x^2-1) for (-1 < x < 1). f-inverse is now a completely valid function, and (f-inverse ...

Sal explains how to understand inverse functions and their graphical relationship.

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2x^3 for x > 0 or f(x) = (x+1)/(x–1) for x ≠1.

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