Composition of Functions Weekly HW

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What is the composition of functions?

Back

The composition of functions is the process of applying one function to the results of another function. It is denoted as (f o g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

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How do you evaluate h(g(2)) if h(x) = -4x + 3 and g(x) = 2x + 3?

Back

First, evaluate g(2): g(2) = 2(2) + 3 = 7. Then, evaluate h(7): h(7) = -4(7) + 3 = -28 + 3 = -25.

Tags

CCSS.HSF-BF.A.1C

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What is the value of f(g(2)) if f(x) = 3x + 6 and g(x) = 2x + 3?

Back

First, evaluate g(2): g(2) = 2(2) + 3 = 7. Then, evaluate f(7): f(7) = 3(7) + 6 = 21 + 6 = 27.

Tags

CCSS.HSF-BF.A.1C

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How do you find f(g(-1)) if f(x) = 3x + 6 and g(x) = 2x + 3?

Back

First, evaluate g(-1): g(-1) = 2(-1) + 3 = 1. Then, evaluate f(1): f(1) = 3(1) + 6 = 3 + 6 = 9.

Tags

CCSS.HSF-BF.A.1C

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What is the formula for f(g(x)) if f(x) = 3x + 6 and g(x) = 2x + 3?

Back

f(g(x)) = f(2x + 3) = 3(2x + 3) + 6 = 6x + 9 + 6 = 6x + 15.

Tags

CCSS.HSF-BF.A.1C

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What does f o g(-3) represent?

Back

f o g(-3) represents the composition of functions f and g evaluated at -3, which means first applying g to -3 and then applying f to the result.

Tags

CCSS.HSF-BF.A.1C

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How do you evaluate h o f(0) if h(x) = -4x + 3 and f(x) = x - 4?

Back

First, evaluate f(0): f(0) = 0 - 4 = -4. Then, evaluate h(-4): h(-4) = -4(-4) + 3 = 16 + 3 = 19.

Tags

CCSS.HSF-BF.A.1C

Front

What is the significance of the order of functions in composition?

Back

The order of functions in composition matters because (f o g)(x) is not necessarily equal to (g o f)(x). The output of g becomes the input of f.

Tags

CCSS.HSF-BF.A.1C

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What is the domain of the composition of functions?

Back

The domain of the composition f o g is the set of all x in the domain of g such that g(x) is in the domain of f.

Tags

CCSS.HSF-BF.A.1B

Front

How do you find the range of a composition of functions?

Back

The range of the composition f o g is determined by the range of g and how it maps into the domain of f.

Tags

CCSS.HSF-BF.A.1B