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Composition of Functions 1
Functions - Finding Unknown
Composition of Functions 2
Notation
Misc.
100
f(x) = 4x + 10. g(x) = 3. Evaluate f(g(x)).
What is 22
100
f(x) = x + 11. Find x when f(x) = 20.
What is x = 9
100
h(x) = 5. g(x) = 2x + 6. Evaluate g(h(x)).
What is 16
100
To read the equation, you say h of x equals 2x plus 1.
What is h(x) = 2x + 1
100
f(x) = (1/4)x. Evaluate f(32).
What is 8
200
f(x) = 8. h(x) = (1/2)x + 20. Evaluate h(f(x)).
What is 24
200
h(x) = 10/x. Find x when h(x) = 5.
What is x = 2
200
h(x) = 3x. f(x) = x + 5. Evaluate f(h(2)).
What is 11
200
This does not mean multiplication.
What is parentheses
200
Using function notation, this represents the output of a function.
What is f(x)
300
g(x) = 2x^2 + 4. h(x) = 3. Evaluate g(h(x)).
What is 22
300
g(x) = 4x + 2. Find x when g(x) = 3.
What is x = 1/4
300
g(x) = 7. f(x) = 3x + 3. Evaluate f(g(x)).
What is 24
300
This part of the composition is evaluated first.
What is inner parentheses.
300
f(x) = 20. g(x) = (1/4)x + 1. Evaluate g(f(x)).
What is 6
400
d(x) = 6. e(x) = |x - 17|. Evaluate e(d(x)).
What is 11
400
f(x) = x^2 + 8. Find x when f(x) = 17.
What is x = +/- 3
400
g(x) = 4. f(x) = x^2 + 2. Evaluate (f ○ g)(x).
What is 18
400
This means you substitute the output of g(x) into f(x).
What is (f ○ g)(x) or f(g(x))
400
h(x) = 3x^3 + 10. g(x) = (1/2)x + 1. Evaluate h(g(2)).
What is 34
500
f(x) = 2. g(x) = (1/8)x^3 + 5. Evaluate g(f(x)).
What is 6
500
b(x) = (1/2)x^2 + 3. Find x when b(x) = 11.
What is x = +/- 4
500
d(x) = 4. h(x) = (1/2)x^2 + 13. Evaluate (h ○ d)(x).
What is 21
500
This notation tells you to find the input value of a function when the output value is 6.
What is f(x) = 6.
500
f(x) = (1/25)x^2 + 4. g(x) = 2x + 6. Evaluate f(g(2)).
What is 8