– [Voiceover] Let’s say that

f of x is equal to two x minus three, and g of x, g of x is equal to 1/2 x plus three. What I wanna do in this video is evaluate what f of g of x is, and then I wanna evaluate

what g of f of x is. So first, I wanna evaluate f of g of x, and then I’m gonna evaluate

the other way around. I’m gonna evaluate g of f of x. But let’s evaluate f of g of x first. And I, like always, encourage

you to pause the video and see if you can work through it. This is going to be equal to, f of g of x is going to be equal to, wherever we see the x in

our definition for f of x, the input now is g of x, so

we’d replace it with the g of x. It’s gonna be two times g of x. Two times g of x minus three. And this is going to

be equal to two times, well, g of x is all of that business, two times 1/2 x plus three, and then we have the minus three. And now we can distribute this two, two times 1/2 x is just

going to be equal to x. Two times three is going to be six. So x plus six minus three. This is going to equal x plus three. X plus three, all right, interesting. That’s f of g of x. Now let’s think about what

g of f of x is going to be. So g of, our input, instead of being,

instead of calling our input x, we’re gonna call our input f of x. So g of f of x is going to be equal to 1/2 times our input, which

in this case is f of x. 1/2 time f of x plus three. You can view the x up

here as the placeholder for whatever our input happens to be. And now our input is going to be f of x. And so, this is going to

be equal to 1/2 times, what is f of x? It is two x minus three. So, two times x minus three, and we have a plus three. And now we can distribute the 1/2. 1/2 times two x is going to be x. 1/2 times negative three is negative 3/2s. And then we have a plus three. So let’s see, three is

the same thing as 6/2s. So 6/2s minus 3/2s is going to be 3/2s. So this is going to be

equal to x plus 3/2s. So notice, we definitely

got different things for f of g of x and g of f of x. And we also didn’t do a round trip. We didn’t go back to x. So we know that these are

not inverses of each other. In fact, we just have to

do either this or that to know that they’re not

inverses of each other. These are not inverses. So we write it this way. F of x does not equal the inverse of g of x. And g of x does not equal the inverse of f of x. In order for them to be inverses, if you have an x value right over here, and if you apply g to it,

if you input it into g, and then that takes you to g of x, so that takes you to g

of x right over here, so that’s the function g, and then you apply f to it, you would have to get

back to the same place. So g inverse would get us back to the same place. And clearly, we did not

get back to the same place. We didn’t get back to x, we

got back to x plus three. Same thing over here. We see that we did not get, we did not go get back to x, we got to x plus 3/2s. So they’re definitely not

inverses of each other.

thank you

lol who's early

Thank u for the usefull education

Thank's khan another great video yet again, đź™‚ đź™‚

yay

Could you do some videos on algebra 2? That would be very helpful, thank you.

please try to upload some more lectures on world history.. please try to cover all the remaning portions ..

What software/hardware do you use for your videos?

You can learn alot from me, im good for your bones.

May I ask you, what pen do you use in SmoothDraw ?

Sal you should male a vid on the Gravital Wave theory by Einstein because NASA detected some Gravital waves and dat stuff

What does he use? Like pen and like a tablet or what???