An inverse is NOT called a circular function. Only inverse functions that are circular functions are called circular functions for obvious reasons.
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Assuming that b > 0, it is an inverse power function or an inverse exponential function.
The logarithm function. If you specifically mean the function ex, the inverse function is the natural logarithm. However, functions with bases other than "e" might also be called exponential functions.
The inverse function means the opposite calculation. The inverse function of "add 6" would be "subtract 6".
Range
No. A simple example of this is y = x2; the inverse is x = y2, which is not a function.