Ex: Intro Composite Function Notation Application Problem — Transcript

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1. 0:00Welcome to two introductory application problems  involving composite function notation. A composite
2. 0:06function is when we compose or combine two  functions, and we use the notation given here
3. 0:11below. These are both equivalent, and we say f of  g of x. When composing a function in this form,
4. 0:19it's probably easier to recognize that to  evaluate this composite function, we would
5. 0:24first evaluate function g, the inner function.  Once we determine the output of function g,
6. 0:30we use this value in function  f. To help us remember this,
7. 0:34we can also say f after g of x, again  reminding us to evaluate function g first.
8. 0:43Let's take a look at our first example. The  function c of f gives the average number of
9. 0:49calories burned for walking f floors of  stairs. f of t gives the number of floors
10. 0:56of stairs an average person can walk in  t minutes. What composite function would
11. 1:02you need to evaluate to determine how many  calories a person will burn in 30 minutes?
12. 1:08Notice in this question they're giving us the  time of 30 minutes. Going back to our functions,
13. 1:14notice if we input time in minutes into function  f, it gives us the number of floors of stairs,
14. 1:21which we can then input into function c to  determine the number of calories burned. So,
15. 1:26because we have to evaluate function f of t first,  this will be the inner function in our composite
16. 1:32function. We'll have f of t, but t is 30, so f  of 30. This will give us the number of floors,
17. 1:40which we will then input into function c  to determine the number of calories burned.
18. 1:45So our composite function is c of f of 30,
19. 1:49which we can also write as c after f of 30.  This would be the required composite function.
20. 1:59Now let's take a look at a second example.  c of t gives the cost of cooling a house
21. 2:05in the desert when the average daily  summer temperature is t. d of d gives
22. 2:11the average daily summer temperature on  day d of summer. What composite function
23. 2:17would you use to determine the cost to cool a  house in the desert on the 28th day of summer?
24. 2:23So we want to know the cost to cool a house  when we're given it's the 28th day of summer.
25. 2:29If we evaluate t of 28, this will give us the  average daily summer temperature on that day.
26. 2:36Once we know the average temperature, we  can substitute that into function c to
27. 2:40determine the cost of cooling the house. So  we first want to evaluate function t of d,
28. 2:45or in this case, t of 28. This will be the  inner function. The output of this will be
29. 2:55the average daily summer temperature, which will  be the input into function c, our cost function.
30. 3:01So c of t of 28 is our composite function,  which we can also write as c after t of 28.
31. 3:14These are both equivalent, just written  in different composite function notation.
32. 3:21Okay, I hope you found this helpful!