Inverse Functions | MathHelp.com - Free Educational videos for Students in K-12 | Lumos Learning

Inverse Functions | MathHelp.com - Free Educational videos for Students in k-12


Inverse Functions | MathHelp.com - By MathHelp.com



Transcript
00:0-1 here , were asked to graph the following function and
00:03 use the horizontal line test to determine if it has
00:07 an inverse , and if so , find the inverse
00:10 function and graph it . So let's start by graphing
00:15 the given function F of X equals two x minus
00:19 four . And remember that F of X is the
00:22 same as why . So we can rewrite the function
00:26 as y equals two X -4 . Now we simply
00:31 graph the line y equals two X -4 , Which
00:36 has a y intercept of negative four And a slope
00:40 of two or 2/1 . So we go up to
00:44 and over one plot a second point and graph our
00:49 line which will call F of X . Next we're
00:54 asked to use the horizontal line test to determine if
00:57 the function has an inverse , Since there's no way
01:01 to draw a horizontal line that intersects more than one
01:05 point on the function , the function does have an
01:09 inverse . So we need to find the inverse and
01:13 graph it to find the inverse . We switch the
01:17 X and Y . In the original function Y equals
01:22 two , X minus four . To get x equals
01:26 two , Y -4 . Next we saw for why
01:31 ? So we add four to both sides to get
01:34 X plus four equals two . Why ? And divide
01:38 both sides by two . To get one half X
01:41 plus two equals Y . Next let's flip our equation
01:48 so that why is on the left side and we
01:51 have Y equals one half X plus two . Finally
01:57 , we replace why with the notation that we use
02:01 for the inverse function of F . As shown here
02:05 and remember that were asked to graph the inverse as
02:08 well . So we graph Y equals one half X
02:13 plus two are y intercept is positive too And our
02:18 slope is 1/2 . So we go up one and
02:22 over two plot a second point graph the line and
02:28 label it as the inverse function of F . Notice
02:32 that the graph of the inverse function is a reflection
02:36 of the original function in the line Y equals X
00:0-1 .
Summarizer

DESCRIPTION:

In this example, we’re given a relation in the form of a chart, and we’re asked to find the inverse of the relation, then graph the relation and its inverse. To find the inverse of a relation, we simply switch the x and y values in each point. In other words, the point (1, -4) becomes (-4, 1), the point (2, 0) becomes (0, 2), the point (3, 1) becomes (1, 3), and the point (6, -1) becomes (-1, 6). Next, we’re asked to graph the relation and its inverse, so let’s first graph the relation. Notice that the relation contains the points (1, -4,), (2, 0), (3, 1), and (6, -1). And the inverse of the relation contains the points (-4, 1), (0, 2), (1, 3), and (-1, 6). Finally, it’s important to understand the following relationship between the graph of a relation and its inverse. If we draw a diagonal line through the coordinate system, which is the line that has the equation y = x, notice that the relation and its inverse are mirror images of each other in this line. In other words, the inverse of a relation is the reflection of the original relation in the line y = x.

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