Composing Functions: Techniques and Examples

The video tutorial explains how to substitute values into functions and compose functions in one step. It demonstrates calculating f of G of X and highlights the difference between f of G and G of f. The tutorial also covers alternative notations and domain restrictions, emphasizing the importance of order in function composition.

What do you replace in the function f(x) to find f(3)?

• Replace 3 with f

• Replace x with 3

• Replace 3 with x

• Replace f with 3

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CCSS.HSF.IF.A.2

In the example f(g(2)), what is the first step?

• Substitute 2 into f(x)

• Substitute 2 into g(x)

• Add 2 to g(x)

• Multiply 2 by g(x)

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CCSS.HSF-BF.A.1C

What is the result of f(g(2)) if g(x) = x^2 + 1 and f(x) = 2x - 3?

• 5

• 7

• 10

• 3

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CCSS.HSF-BF.A.1C

How do you find f(g(x)) in one step?

• Multiply f(x) by g(x)

• Substitute f(x) into g(x)

• Substitute g(x) into f(x)

• Add f(x) and g(x)

Tags

CCSS.HSF-BF.A.1C

What is the formula for f(g(x)) if g(x) = x^2 + 1 and f(x) = 2x - 3?

• 2x^2 - 3

• 2x^2 + 1

• 2x^2 + 2

• 2x^2 - 1

Tags

CCSS.HSF-BF.A.1C

What is the difference between f(g(x)) and g(f(x))?

• They are inverses

• They are different operations

• They are always equal

• They are the same

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CCSS.HSF-BF.A.1C

What is g(f(x)) if f(x) = 2x - 3 and g(x) = x^2 + 1?

• 4x^2 - 12x + 1

• 4x^2 - 12x + 11

• 4x^2 - 12x + 9

• 4x^2 - 12x + 10

Tags

CCSS.HSF-BF.A.1C

What does the notation H(f(x)) represent?

• H added to f

• f composed with H

• H composed with f

• H multiplied by f

Tags

CCSS.HSF-BF.A.1C

What is the result of H(f(x)) if H(x) = 3/(x-4) and f(x) = 2x - 3?

• 3/(2x - 4)

• 3/(2x - 7)

• 3/(2x - 3)

• 3/(2x - 1)

Tags

CCSS.HSF-BF.A.1C

What is a restriction on the domain of H(f(x)) if H(x) = 3/(x-4) and f(x) = 2x - 3?

• x cannot be 4

• x cannot be 3/2

• x cannot be 7/2

• x cannot be 2