Evaluating Composite Functions and Inverses

The video tutorial explains how to evaluate composite functions using given functions f(x) and g(x). It demonstrates the process of finding f(g(3)) and g(f(3)) through substitution and calculation. The tutorial also covers the concept of functions and their inverses, showing how to verify if two functions are inverses by using composition. The video provides a clear step-by-step guide to understanding these mathematical concepts.

What is the definition of a composite function?

• A function that is divided by another function.

• A function that is added to another function.

• A function that is multiplied by another function.

• A function that is applied to the result of another function.

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CCSS.HSF-BF.A.1C

What is the first step in evaluating f(g(3))?

• Find g(x).

• Find f(x).

• Find g(3).

• Find f(3).

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CCSS.HSF-BF.A.1C

What is the value of g(3) if g(x) = x^2?

• 9

• 6

• 12

• 3

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CCSS.HSF.IF.A.2

What is the value of f(9) if f(x) = 2x - 3?

• 12

• 21

• 18

• 15

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CCSS.HSF.IF.A.2

What is the first step in evaluating g(f(3))?

• Find g(3).

• Find g(x).

• Find f(x).

• Find f(3).

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CCSS.HSF.IF.A.2

What is the value of f(3) if f(x) = 2x - 3?

• 9

• 3

• 6

• 12

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CCSS.HSF.IF.A.2

What is the value of g(3) if g(x) = x^2?

• 9

• 6

• 3

• 12

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CCSS.HSF.IF.A.2

What must be true for two functions to be inverses of each other?

• f(g(x)) = 0 and g(f(x)) = 0

• f(g(x)) = g(f(x))

• f(g(x)) = x and g(f(x)) = x

• f(x) = g(x)

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CCSS.HSF-BF.B.4B

What is the composite function f(g(x)) if f(x) = 2/3x + 6 and g(x) = 3/2x - 9?

• 2x

• 4x

• x

• 3x

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CCSS.HSF-BF.A.1C

What is the composite function g(f(x)) if f(x) = 2/3x + 6 and g(x) = 3/2x - 9?

• x

• 4x

• 2x

• 3x

Tags

CCSS.HSF-BF.A.1C