Sketch the graph of the inverse of ƒ...

Question

Sketch the graph of the inverse of ƒ.

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. For the given function F, plot the graph of its inverse. So as you can see, the graph that is provided to us by the problem itself, we have two different curves. We have a curve in green and a curve in blue. The curve in green denotes our function of Y equals X. Or equation Y equals X, and then we also have our second curve, which is denoted as Y equals F of X. Awesome. So our curve for Y equals X is just a line passing through the origin point 0.0. And for Y equals F of X, we have a curly curve that's like an elongated S shape. And it appears they intersect, both of these two curves intersect at It appears to be a little bit over -1, but not quite -2. So I like -1. something and. At -1. something. So they both intersect here. I'll label it in red, they intersect at this point right here. Awesome, which is once again about, since it's not quite -2 for either side, so it's like at -1. something negative 1.something, so it's not quite negative 2. So, with that said, Our first step once again is we need to recall and note that the graph of the inverse of F can be obtained by reflecting the graph of F about the line Y equals X. So let us take the following points to help us achieve this. Let's take the points, specifically the coordinate points. 6.2, and note that this is in the XY format for our coordinate points. So let's take the points -6-2. and then let's also take the 20, and lastly, let us also take the 0.3, 1. Fantastic. So let us use these coordinate points to help us create our graph of the inverse of F. So in order to find the new points on the graph of the inverse of F of X, as we should recall a note, we need to Interchange the X and Y values of the above points, and when we do that, we will get the new points which we will get 26, we will get 0.2, and we will also get 1.3. So we now need to take these new coordinate points, and we need to plot them on the graph and draw a smooth curve. Which is reflected, which will be the reflected graph of F of X about the line, as we discussed, Y equals X, and this will be our final graph that we're trying to solve for our final answer, which is the graph of the inverse. So that's what we're ultimately trying to solve for for this particular practice problem. So, with that said, when we take This information and we plot it into our graph which I use some graphing software to create the following digitized graph. And as you can see, our new curve, which is the inverse curve, which once again this is the final answer we're ultimately trying to solve for is represented in red now, whereas our original curve for Y equals F of X is in blue. And then we have our line, which is Y equals X, represented as a black curve. So once again, our new inverse graph of our original function is going to be a red curve, and we have our points listed. We have at 1.3, 0.2, and 2 and 6. Awesome. And our new way of writing, and in case it's hard to read, our new way of writing our inverse function. will be Y equals the power of -1 X. So this is our inverse function, and this will be for our red curve, which will put a red box around our function for the inverse function. And that's it. That is how you solve for this particular problem. So this problem is very easy to solve as long as you have a strong understanding of the background. Math required to plot the inverse. So once again, the hardest part or the hardest thing you need to remember is you need to note that when you're trying to find the new points on the graph for the inverse of F of X, you need to interchange the values of X and Y for our above points that you draw from the graph that's provided to you by the prom itself. So that's the hardest point. Other than that, it's pretty cut and dry. So once you find the interchange of the X and Y values, you take those points, you plot it on your coordinate plane, and you connect them with a smooth curve and that will be your new inverse function. And that's it. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Sketch the graph of the inverse of ƒ. <IMAGE>

Key Concepts

Inverse Functions

Graphing Functions and Their Inverses

Domain and Range

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