This makes finding the domain and range not so tricky! We do this a lot in everyday life, without really thinking about it. How to get the Inverse of a Function step-by-step, algebra videos, examples and solutions, What is a one-to-one function, What is the Inverse of a Function, Find the Inverse of a Square Root Function with Domain and Range, show algebraically or graphically that a function does not have an inverse, Find the Inverse Function of an Exponential Function Uses worked examples to demonstrate how to find the inverse of a function, including taking domain restrictions into account. The inverse function, therefore, moves through (–2, 0), (1, 1), and (4, 2). < 0. Inverse Functions undo each other, like addition and subtraction or multiplication and division or a square and a square root, and help us to make mathematical “u-turns”. google_ad_slot = "1348547343"; For a function   f(x), A function accepts values, performs particular operations on these values and generates an output. the inverse is denoted   f -1(x). the algebra:  Copyright As it stands the function above does not have an inverse, because some y-values will have more than one x-value. The For example, the inverse of \(f(x) = 3x^2\) cannot be written as \(f^{-1}(x) = \pm \sqrt{\frac{1}{3}x}\) as it is not a function. > 0; the Section. Notation used … >>, Stapel, Elizabeth. Original function; f(x) = 3x - 5: First multiply by 3: Then subtract 5 : Inverse function; f -1 (x) = First add 5 Then divide by 3 Not all functions have inverses. Detailed solutions are also presented. range will be y Purplemath.  |  Return to Index  Next But the restriction is useful in this /* 160x600, created 06 Jan 2009 */ However, this page will look at some examples of functions that do have an inverse, and how to approach finding said inverse. inside the square root. Intro to Finding the Inverse of a Function Before you work on a find the inverse of a function examples, let’s quickly review some important information: Notation: The following notation is used to denote a function (left) and it’s inverse (right). State its domain and range. Then Next Section .