Pöördtehe

Pöördtehe, often translated as inverse operation or reverse operation, is a fundamental concept in mathematics referring to an operation that undoes the effect of another operation. For every mathematical operation, there exists a corresponding pöördtehe that reverses its action.

The most common examples of pöördtehe involve basic arithmetic. Addition and subtraction are pöördtehed of each other. For instance, if you add 5 to a number, you can subtract 5 to return to the original number. Similarly, multiplication and division are pöördtehed. Multiplying a non-zero number by 3 can be undone by dividing by 3.

In algebra, pöördtehed are crucial for solving equations. When isolating a variable, we apply the pöördtehe of the operation being performed on that variable. For example, to solve x + 7 = 10, we apply the pöördtehe of addition, subtraction, by subtracting 7 from both sides.

Beyond arithmetic and algebra, the concept extends to other areas of mathematics. For instance, exponentiation and taking roots are pöördtehed. The square root operation undoes squaring a non-negative number. Differentiation and integration are also considered pöördtehed in calculus, with integration being the pöördtehe of differentiation.

Understanding pöördtehed is essential for developing problem-solving skills and for comprehending more advanced mathematical concepts. It provides a systematic way to manipulate mathematical expressions and solve equations by reversing the steps taken.