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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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Inverse functions undo each other when we compose them. We can compose functions by making the output of one function the input of another one. This simple-yet-rich idea opens up a world of fascinating applications.

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 ...

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 or f(x) = (x+1)/(x-1) for x ≠ 1.

Determine an inverse function, when it exists, for a given function over its domain or a subset of its domain and represent the inverse using multiple representations.

Learn algebra with Khan Academy's interactive lessons and practice problems.

(+) Read values of an inverse function from a graph or a table, given that the function has an inverse.

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