31. This is guaranteed to hold if " ? " is continuously differentiable by the inverse function theorem. 32. Typically, one is not interested in " ? " itself, but in its inverse function . 33. The notation " f " " 1 should not be confused with that for inverse function . 34. Inverse functions are closely related to the original functions : the differentiable, so is its inverse function,.35. Inverse functions are closely related to the original functions : the differentiable, so is its inverse function ,. 36. The fixed point theorem is often used to prove the inverse function theorem on complete metric spaces such as Banach spaces. 37. At high frequencies, the PIN diode appears as a resistor whose resistance is an inverse function of its forward current. 38. Then the natural logarithm could be recognized as the inverse function to the transcendental function e " x ". 39. While the notation might be misunderstood, certainly denotes the multiplicative inverse of and has nothing to do with the inverse function of. 40. Intuitively, an inverse function is obtained from " f " by interchanging the roles of the dependent and independent variables.
