 This video is part two of composition of functions. Alright, now some fun with some graphs. Remember we use this value in for Q. Those two things go together. So I come into Q, Q is pink by the way, I come over to negative 4, that's the input. So negative 4 is my input and Q of negative 4 is going to be equal to, Q is down here so I have negative 4. So that means that I'm going to do P of negative 4. So I'm still at negative 4 and go back up to negative 4 because now that's my input and I go and find my P function and it tells me that it's equal to positive 4, that's a positive 4. So let's try again. Okay, so Q of 1, I come over here and Q of 1 down here is 1, 2, 3, negative 3. So now I need to say P of negative 3 and so I go, X is now negative 3, the input, it's a 1, 2, 3 and I find, go to the blue and come down here and it's right here so that would be negative 1. Alright, let's try another one. P of 7, you can put a function within itself. So P of 7, so I come over here to 7 and the P is the blue. That's equal to 6 and then that means that I want to find P of 6 because remember this goes in here and P of 6, 4, 5, 6 is going to give me a value of 2. P of 2 is going to be P is the blue. I come to 2 and the X and I go up to the blue and it looks like 1, 2, 3, 4, 5. So now I have to do Q of 5 because again remember this number becomes the input of the first function. I come over to 5 and I look at the Q and it's going to be equal to 6. Finally I have Q of negative 1, so X is negative 1, Q is the pink one, so that's equal to 3 and then I need to do Q of 3 because again this 3 becomes that 3 and Q of 1, 2, 3 looks like 1, 2, 3, negative 3. Alright, I think we have one more thing to do and that's to look at a story problem. So due to a light and strike a force prior brings a burn and is spreading outward in a shape that is roughly circular, the radius of the circle is modeled by the function r of t equal to 2t, t is in minutes, r is in meters. So find the radius of the circle after 2 minutes for the radius that be r of 2 and that would be 2 times 2 so it's going to be 4 meters since r is in meters. In a sense it says find the area of the circle, well you need to know the area is equal to pi r squared. We have 2 is our radius so it's pi times 2 times 2 as the radius squared the area would be to 16 pi with meters squared. So now I want to write the function a of r of t. I'm going to call it a of t. That means I'm going to end the a function. I'm going to put in the r and remember r up here is 2t. I have pi and then I'm going to put my r in there and I'm going to square it. My r in there is 2t. So if I simplify it I'm going to have 2 squared is 4, t squared is t squared times pi and that would be my a. So now I want to use this function to find the area of the circle in 2 minutes. a is equal to 4 times 2 squared times pi. That's 4 times 4 which is 16 pi meters squared. Notice that's really what we did above. First we figured out the radius and then we figured out the area using that same value. We can do it separately or we can make it one function with compositions which is a little bit easier to use. Okay, one more composition question. On a trip to Europe, Megan had to convert American dollars to euros and she had this function. X is number of dollars, the function is equivalent to number of euros and then later she does it with Japanese yen using the functions that you see there. So the first part asks us just to convert the hundred dollars to euros to remember X is a number of equivalent dollars. So we just have E of 100 and that will be equal to 1.12 times 100. You multiply by 100 you move the decimal to places. So that's equal to 112 euro. So now the one is to convert our answer which was 112 in part a to Japanese yen and that's this equation here. So we have Y of 112 is equal to 1061 times 112 and when we do that we end up with a lot of yen. 1, 1, 8, 8, 3, 2, 118, 832 yen. We see now we want to express yen as a function of dollars. So yen doing this one is we have M of X, let's start there. So M of X is equal to and then we have the yen function which says 1061 times but we have to plug in there the E function which is 1.12X. So M of X is going to be equal to 1188.32X. So remember that number because we're going to need to use it here. M of X is equal to 1188.32X and we want to convert the dollars and remember come back to here. We have this is a function of dollars so that means that this X is going to be dollars. So we want M of 100. When you multiply by 100 you move the decimal to places and you get 118,832 and do the answers agree? Yes they do.