1. AM5.2b To Form Composite Functions
AM5.2b To Form Composite Functions
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2. Active Learning Assignment Questions?
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3. To clarify: To find: If f(x) = x + 2 Then f(x2 – 3) = (x2 – 3) + 2
LESSON: To form composite functions.
To clarify:
To find:
If f(x) = x + 2
( )
Then f(x2 – 3) =
(x2 – 3) + 2
= x2 – 3 + 2
 (f ◦ g)(x) = x2 – 1

4. To clarify: To find: If f(x) = x + 2 Then f(x2 – 3) = (x2 – 3) + 2
Again, to dissect the problem:
Determine what we need:
To clarify:
Set up the given:
To find:
If f(x) = x + 2
( )
Replace “x”:
Then f(x2 – 3) =
(x2 – 3) + 2
Simplify:
= x2 – 3 + 2
 (f ◦ g)(x) = x2 – 1

5. BAM! g(2) = 22 – 3 = 1 f(1) = 1 + 2 = 3  (f ◦ g)(x) = x2 – 1
Well, we started with (Don’t copy, just observe):
And we wanted to find: f(g(2)) ?
g(2) = 22 – 3
= 1
f(1) = 1 + 2
= 3
 (f ◦ g)(x) = x2 – 1
Now, we ended with:
(f ◦ g)(2) = 22 – 1
How about:
(f ◦ g)(2) ?
BAM!
= 3
SAME ANSWER!

6. To clarify: To find: If g(x) = x 2 Then g(2x – 5) = (2x – 5)2
Try:
Determine what we need:
To clarify:
Set up the given:
To find:
If g(x) = x 2
( )
Replace “x”:
Then g(2x – 5) =
(2x – 5)2
Simplify:
= (2x – 5) (2x – 5)
FOIL, and you get:
(g ◦ f)(x) = 4x2 – 20x + 25

7. FOIL, simplify, and you get: = 9x2 + 6x + 1 – 2
Try:
To clarify:
To find:
If g(x) = x 2 – 2
( )
Then g(3x + 1) =
(3x + 1)2 – 2
FOIL, simplify, and you get:
= 9x2 + 6x + 1 – 2
(g ◦ f)(x) = 9x2 + 6x – 1

8. Active Learning Assignment:
P. 128: (CE) 9b, 10b
P. 130: (WE) 33, 35
WOW:
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