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What is the image of the x power of e and the e -x power? What is the relationship between two reciprocal function images?
The image is as shown in the figure below, and there is no certain relationship between the reciprocal two function images.

Function was originally translated by Li, a mathematician of Qing Dynasty in China, in his book Algebra. He translated this way because "whoever believes in this variable is the function of that variable", that is, the function means that one quantity changes with another quantity, or that one quantity contains another quantity.

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/kloc-in the 0/7th century, Galileo almost completely contained the concept of the relationship between functions or variables in his book Two New Sciences, and expressed the relationship between functions in words and proportional languages.

Descartes noticed the dependence of one variable on another in his analytic geometry around 1637, but he didn't realize the need to refine the concept of function at that time, so no one knew the general meaning of function until Newton and Leibniz established calculus in the late17th century, and most functions were studied as curves.