Mathematics in Plain English - What is an inverse function?

In mathematics, an inverse function largely undone, what is the function date. If we think in terms of domain and range, if a certain function has a value of x being in the domain of a y-value of the range, then its inverse function takes the value y in the same field and sends it to the value x in the domain.

Inverse functions are important in mathematics, because in some problems, weknow what the range is, and we need that this domain is value to be determined. For example, in some problems of trigonometry we know the value that the sine or cosine of produce and we want to know what angle produces these values. This can happen if you want to build, say, a right triangle given the lengths of the sides and want, we measure the angle that know these pages are hosted.

To find the inverse function of a particular function, theFunction at hand is a being-a. If you have not read my article on this topic, are the definition of a one-on-a function to repeat here: one-to-one functions that exceed the horizontal line test, ie, it can never happen that two different values ​​of x in the domain sent on the same y value in the area. This condition must be satisfied to find an inverse function, because if not, then there would beEssentially two paths to send back the value of y (y could return to one of several x values ​​from which it came.) As a result lead to an ill-defined inverse function would be.

Mathematics in Plain English - What is an inverse function?

Once we find a function that one-on-one to solve, we are able to reverse by switching the x and y values ​​in the equation for y. To see this, let's take a simple example, linearFunction y = 3x - 2 All linear functions are one-to-one. So we can solve x and y switch, and x = y. Hence we have 3y -2; solution for y we have y = (x + 2) / 3 This is all you need to do.

To prove that this is really the function that takes a particular value x and sends it back where it came from, let's examine a concrete example.Let x = 10 In the given function y = 3x - 2, This gives y = 28 The inverse Function should send this back to the value of 28 to 10. If you plug 28 in the function y = (x + 2) / 3 You see that you get to 10 so the inverse function is doing what it was designed to do.

For more complicated functions, theinverse can be found it extremely difficult if not impossible at all. For these situations are based on sophisticated mathematical tools and methods. In most cases, however, a certain function and its inverse are not polar opposites such as: If the function requires a traveler to the North Pole, he is the reverse back to the South Pole. What a nice guy, this inverse function?

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