The Inverse Function

Pure Mathematics — Second Secondary

The idea of an inverse function

The inverse of a function f, written f⁻¹, is the function that reverses the action of f. If f(a) = b, then f⁻¹(b) = a.
The inverse satisfies two properties:

f⁻¹(f(x)) = x for every x in the domain of f.
f(f⁻¹(x)) = x for every x in the domain of f⁻¹.
Warning the notation f−1 means the inverse function, not the reciprocal. In general f−1(x) is not equal to 1/f(x).

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