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Bell Ringer

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x2+4

x-3

x+2

x+1Find the Area and Perimeter.Bell Ringer

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Compositions with Functions

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Definitions:Domain: all possible x values of a function

Range: all possible y values of a function

Composition of Functions: the range of one function becomes the domain of another function

(f g)(x) = f(g(x))

Definitions:Domain: all possible x values of a function

Range: all possible y values of a function

Composition of Functions: the range of one function becomes the domain of another function

(f g)(x) = f(g(x))

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Algebraically:

(h ○ g)(x) (g ○ h)(x)

g(x) = 2x and h(x) = x + 2

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Algebraically:

f(x) = 3x2 – x + 4 and g(x) = 2x – 1

(f ○ g)(x) (g ○ f)(x)

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Algebraically:

f(x) = x2 + 2x + 3 and g(x) = x + 5

(f(g(x)) (g(f(x))

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Practice:

1. (f(g(1))

3. (g – f)(x)

f(x) = 3x, g(x) = x + 4, and h(x) = x2 – 1 Find each value:

2. (g ○ h)(0)

4. (f(h(x))

5. (f(g(x)) 6. (h ○ f)(x)

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f(x) = x2 + 2x + 3 and g(x) = x + 5

(f/g)(x) (f*g)(x)

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f(x) = 3x, g(x) = x + 4, and h(x) = x2 – 1

(f­h)(x) (h/g)(x)

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