yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Reading inverse values from a graph


3m read
·Nov 10, 2024

  • [Instructor] We're told the following graph shows y is equal to f of x. All right. And then the first question they say is, "What appears to be the value of f inverse of two?" Pause the video and see if you can have a go at that.

All right, now let's work through this together. So it's important to realize they're not asking us what f of two is. They're asking us f inverse of two. f of two we would say, "Okay, when x is equal to two that's the input into our function." And then the graph tells us that f of two it looks like it might be a little bit more than 2.5. Maybe it's approximately 2.6. But that's not what they're asking us. They're asking us f inverse of two.

And just as a reminder of what an inverse function is, if we have some input, x, and we input into our function, f, that is going to output f of x. Now, if we were to input f of x into the inverse function for f, then the output here, which is going to be f inverse of f of x is going to get us back to this original x, is going to be equal to x. So we are really, in this scenario, dealing with this part of this chain of inputs and outputs.

We're saying we want to figure out what f inverse of two is. So this part, right over here is going to be equal to two. So we're saying when f of x is equal to two, what is the corresponding x? So when f of x is equal to two, what is the corresponding x? We get four. So let's write that down. f inverse of two is equal to four.

So when x is equal to four, you input that f of four is equal to two or f inverse of two is equal to four. Now the next part they say, "Sketch the graph of y is equal to f inverse of x." So an important thing to realize is if we're saying that b is equal to f of a which implies that the point a, b is on the graph of f, then we're dealing with f inverse.

We would know that a would be equal to f inverse of b. You can think about swapping these two, the a and the b's here, which means that b, a would be on f inverse. So any coordinate point that's on our original graph f, if you swap the x and the y, that's going to be on our f inverse. So let's just pick some points. And once again, they're just saying sketch, so it doesn't have to be perfect.

So if we look at this point right over here, that looks like the point -10, maybe it looks like 3.4. Well, then that means if we swap that x and y it'll be on the graph of f inverse. So if we go to 3.4, and then -10, so it gets us right about there, that would be on the graph of f inverse.

Now, if we went to, let's say this point right over here. This is the point -2, 3. So if -2, 3 is on the graph of f, then 3, -2 would be on the inverse. So 3, -2 would be on the inverse right over there. Let's pick a few more points. So we have this point right over here, 4, 2 which would be on the graph of f, which means that 2, 4 is on the inverse.

So 2, 4, which would be right over there. And then if we look at this point over here which looks like roughly nine, let's just call it 9, -10 maybe it's 9.1, -10. If that's on the graph of f, then if we swap that, -10, maybe 9.1 would be on the inverse -10, 9.1, right over there.

And so then we could connect the dots to try to sketch out what the inverse function is going to look like, the graph of the inverse function. So it's going to look something like that. And you might notice, it looks like it's a reflection about the line y = x. It looks like it's a reflection about that line, which is exactly right.

More Articles

View All
Sign of average rate of change of polynomial | Algebra 2 | Khan Academy
So we are given this function h of x, and we’re asked over which interval does h have a positive average rate of change. So, like always, pause this video and have a go at it before we do this together. All right, now let’s work through this together. To…
Finding a Cancer Killer | Breakthrough
NARRATOR: Working out of the University of Pennsylvania, Dr. June has been developing a new technology to leverage the immune system’s T-cells to fight and kill leukemia in mice. [squeaking] CARL JUNE: Yeah. I have been through a long journey. So I was a…
Adjective order | The parts of speech | Grammar | Khan Academy
So, Grom Marians, if you’re a native English speaker, the phrase “French old white house” might seem a little weird to you. If you’re not a native English speaker, it might not. This is something that I didn’t really know about before I started preparing …
The Saltwater Croc Threat | Primal Survivor
I’m traveling along the Araund River in Papua New Guinea, and I’m now over halfway to my destination—a village that a generation ago practiced one of the darkest customs of all: cannibalism. A place where young men would be sent out to bring back the head…
Go with what you can get started on most quickly. And get that first user.
Here’s a question: I have lots of startup ideas. How do I choose the one to work on? Uh, common problem. There’s too many choices; there’s lots of choices in the world. You don’t know what to focus on. You know, there’s different algorithms you can use.…
Mr. Freeman, part 63
All right, hot-shots, no small talk or bullshit today! Just cold reality and stark, naked truth. Don’t wanna know, or friggin’ scared? Door’s there! Whattaya waiting for? Thanks for sharing, get the hell out! I’ve had it with your snobby fed-up attitude a…