Reverse functions. Theory and tasks

The theory and methods of solving problems of various complexity on the topic "reverse function" are described. In order to facilitate the perception and assimilation of this complex topic, in the first part of the work, the argument of the monotonous function in general form was studied, and then its basic private cases were introduced and investigated according to a single plan: Arksinus, Arkkosinus, Arctankogenes, Arkkotangen, Arithmetic root and logarithm. In the second part, the reverse function is in general form, the methodology for obtaining it and six basic private cases, including reverse trigonometric and logarithmic functions are described. The presentation of the theory is fixed by the analysis of typical and non -standard tasks, including from the practice of the exam. Additional insufficiently known formulas (for example, in logarithm tasks) and effective methods for replacing the multipliers and the rampers of ODZs in complex inequalities with reverse trigonometric and other functions are also used. The publication is intended for a wide range of readers: schoolchildren, applicants, students, teachers and all fans of mathematics