In mathematics, an inverse refers to the opposite of another operation. It can have different meanings depending on the context. Here are some examples:
- Inverse operation: Operations that are opposite of each other are known as inverse operations. For example, division is the inverse operation of multiplication and subtraction is the inverse operation of addition.
- Additive inverse: The additive inverse is what we add to a number to get zero. For example, the additive inverse of -5 is +5, because -5 + 5 = 0.
- Multiplicative inverse: The multiplicative inverse is what we multiply a number by to get 1. It is the reciprocal of a number. For example, the multiplicative inverse of 5 is 1/5, because 5 × 1/5 = 1.
- Inverse function: An inverse function is a function that undoes the operation of another function. The inverse of a function f exists if and only if f is bijective, and if it exists, is denoted by f^-1. For example, if f(x) = 5x - 7, its inverse function is defined by g(y) = (y + 7)/5, which undoes the operation of f.