Supplement: Do you want to use reduction to absurdity? Try asking: Please help me prove numbness! There are pictures and miscellaneous paintings? Answer: the images of the inverse function and the original function are symmetrical about y = X. Ask: What about the proof? Answer: The inverse function and the original function have the same monotonicity. If they do not have the same monotonicity, they cannot be inverse functions. Assuming that the inverse function is monotonous and the original function is not monotonous, then this inverse function has no inverse function (that is, the original function) and has the same monotonicity contradiction with the inverse function and the original function, so the assumption is untenable, that is, the inverse function has the same monotonicity with the original function. Question: What about the proof? Answer: The inverse function and the original function have the same monotonicity. If they do not have the same monotonicity, they cannot be inverse functions. It is proved that if the inverse function is monotonic and the original function is not monotonic, then this inverse function has no inverse function (that is, the original function) and has the same monotonic contradiction with the inverse function and the original function, so the assumption is untenable, that is, the inverse function has the same monotonicity with the original function. Q: What about its image? I don't understand what you said. Answer: Draw one yourself, for example, y=5x, and its inverse function is y= 1/5x. Q: Is the image hyperbola or! ?