So how do we prove that a given function has an inverse? Functions that have inverse are called one-to-one functions.Ī function is said to be one-to-one if, for each number y in the range of f, there is exactly one number x in the domain of f such that f (x) = y. We check whether or not a function has an inverse in order to avoid wasting time trying to find something that does not exist. Since not all functions have an inverse, it is therefore important to check whether a function has an inverse before embarking on determining its inverse. ![]() This article will discuss how to find the inverse of a function. One thing to note about the inverse function is that the inverse of a function is not the same as its reciprocal, i.e., f – 1 (x) ≠ 1/ f(x). For example, if f (x) and g (x) are inverses of each other, then we can symbolically represent this statement as: We use the symbol f − 1 to denote an inverse function. In simple words, the inverse function is obtained by swapping the (x, y) of the original function to (y, x). ![]() The inverse of a function can be viewed as reflecting the original function over the line y = x. In mathematics, an inverse function is a function that undoes the action of another function.įor example, addition and multiplication are the inverse of subtraction and division, respectively. Inverse of a Function – Explanation & Examples What is an inverse function?
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