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

Evaluating composite functions | Mathematics III | High School Math | Khan Academy


3m read
·Nov 11, 2024

  • [Voiceover] So, we're told that g of x is equal to x squared plus 5 x minus 3 and h of y is equal to 3 times y minus 1 squared, minus 5.

And then, we're asked, what is h of g of negative 6?

And the way it's written might look a little strange to you. This little circle that we have in between the h and the g, that's our function composition symbol.

So, function, function composition, composition, composition symbol. And one way to rewrite this, it might make a little bit more sense.

So, this h of g of negative 6. You could rewrite this as, this is going to be the same thing as g of negative 6, and then h of that.

So, h of g of negative 6. Notice, I spoke this out the same way that I said this.

This is h of g of negative 6. This is h of g of negative 6. I find the second notation far more intuitive, but it's good to become familiar with this function composition notation, this little circle, because you might see that sometime and you shouldn't stress, it's just the same thing as what we have right over here.

Now, what is h of g of negative 6? Well, we just have to remind ourselves that this means that we're going to take the number negative 6, we're going to input it into our function g, and then that will output g of negative 6, whatever that number is, we'll figure it out in a second, and then we're going to input that into our function h.

We're going to input that into our function h. And then, what we output is going to be h of g of negative six, which is what we want to figure out.

h of g of negative 6. So, we just have to do it one step at a time.

A lot of times, when you first start looking at these function compositions, it seems really convoluted and confusing, but you just have to, I want you to take a breath and take it one step at a time.

Well, let's figure out what g of negative 6 is. It's going to evaluate to a number in this case.

And then, we input that number into the function h, and then we'll figure out another -- that's going to map to another number.

So, g of negative 6. Let's figure that out. g of negative 6 is equal to negative 6 squared, plus 5 times negative 6, minus 3, which is equal to positive 36, minus 30, minus 3.

So, that's equal to what? 36 minus 33, which is equal to 3.

So, g of negative 6 is equal to 3. g of negative 6 is equal to 3. g of negative 6 is equal to 3.

You input negative 6 into g, it outputs 3.

And so, h of g of negative 6 has now simplified to just h of 3 because g of negative 6 is 3.

So, let's figure out what h of 3 is. h of 3 -- notice, whatever we outputted from g, we're inputting that now into h.

So, that's the number 3, so h of 3 is going to be 3 times 3 minus 1, 3 minus 1 squared, minus 5, which is equal to 3 times 2 squared, this is 2 right over here, minus 5, which is equal to 3 times 4 minus 5, which is equal to 12 minus 5, which is equal to 7.

And we're done.

So, you input negative 6 into g, you get 3.

And then, you take that output from g and you put it into h and you get 7.

So, this right over here is 7. All of this has come out to be equal to 7.

So, h of g of negative 6 is equal to 7. h of g of negative 6 is equal to 7.

Input negative 6 into g, take that output and input it into h, and you're gonna get 7.

More Articles

View All
Reversion to the Mean
It’s a cold winter morning. You wake up fresh and rested. You get ready and go to the nearest cafe to start the day with a cup of coffee. You order your favorite: an iced caramel latte. As you wait for your coffee, you make small talk with the stranger ne…
Reprogramming Perception - Tech+Art | Genius: Picasso
I like to challenge my audience with sensory experiences that can almost feel threatening. I use hair, spit, semen, blood. Why do you find it disgusting? Why is that normal? Why are things so sanitized? I think, as an artist, I’m really interested in all …
Eyes on Orcas | Continent 7: Antarctica
[music playing] [splash] [shout] NARRATOR: After a season of frustration– BEN SHARP: Right there. NARRATOR: –Regina and her team have a killer whale in sight. BEN SHARP: He’s coming towards the edge. NARRATOR: Now, they just need it to be in range. …
This Is Why Discord Is Dangerous
On the 13th of April 2023, a 21 year old member of the U.S Air Force National Guard, Jack Tashira, was arrested on live TV for leaking classified documents. Tashira had shared classified information about the war in Ukraine with his Discord group, Thug Sh…
How to finance a private jet
Will you take bank financing on the air? Correct. Okay, so that’s a key question because a bank, if they’re going to loan money to you, usually what they say is the term of the loan plus the age of the airplane should not exceed 20 years. So, meaning at…
Why “Looking Poor” Is Important
What’s up you guys, it’s Graham here. In the last few months, you might have come across one of these videos: the importance of looking poor. After all, when you really dig into it, it is insane how many people these days are pretending to be rich, diggi…