The inverses of hyperbolic function are the area hyperbolic functions. They are called area functions becasue they compute the area of a sector of the unit hyperbola x2 − y2 = 1 This is similar to the inverse trig functions which correspond to arclength of a sector on the unit circle
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The inverse of the inverse is the original function, so that the product of the two functions is equivalent to the identity function on the appropriate domain. The domain of a function is the range of the inverse function. The range of a function is the domain of the inverse function.
The original function's RANGE becomes the inverse function's domain.
The inverse of the cubic function is the cube root function.
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No, an function only contains a certain amount of vertices; leaving a logarithmic function to NOT be the inverse of an exponential function.