Functions: Composite Functions 1

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Christian Lawson-Perfect 2 years, 6 months ago

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Ben McGovern 4 years, 7 months ago

Created this as a copy of Functions: Evaluating Functions 3.

Name	Status	Author	Last Modified
Functions: Evaluating Functions 2	Ready to use	Ben McGovern	10/10/2022 13:02
Functions: Evaluating Functions 3	Ready to use	Ben McGovern	10/10/2022 13:02
Functions: Composite Functions 1	Ready to use	Ben McGovern	10/10/2022 13:00
Functions: Composite Functions 2	Ready to use	Ben McGovern	10/10/2022 13:00
Functions: Composite Functions 3a	Ready to use	Ben McGovern	10/10/2022 13:00
Functions: Composite Functions 3b	Ready to use	Ben McGovern	24/04/2023 14:32
Functions: Composite Functions 4a	Ready to use	Ben McGovern	10/10/2022 13:00
Functions: Composite Functions 4b	Ready to use	Ben McGovern	10/10/2022 13:00
Functions: Evaluating Composite Functions 1 - Modulus Functions	Ready to use	Ben McGovern	10/10/2022 13:02
Functions: Composite Functions 5 - Modulus Functions	Ready to use	Ben McGovern	10/10/2022 13:01
CA7 Composite functions	Ready to use	Megan Oliver	17/04/2025 09:02

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Question statement

If $f(x)=\simplify{{m}x+{c}}$ and $g(x)=\simplify{{n}x+{d}}$ , find expressions for $f\circ g(x)$ and $g \circ f(x)$ .

Recall: $f \circ g(x) \equiv f(g(x))$ and $g \circ f(x) \equiv g(f(x))$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

n	integer	3
m	integer	2
c	integer	4
d	integer	-3

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1. Gap Gap 0 Mathematical expression
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2. Gap Gap 1. Mathematical expression
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$f \circ g(x)=$ Gap 0

$g \circ f(x)=$ Gap 1.

Advice

To find the composition $f \circ g(x)$ we are substituting the expression for $g(x)$ into the function $f(x)$ , replacing the $x$ -terms with the function $g(x)$ . Similarly, to find the composition $g \circ f(x)$ we are substituting the expression for $f(x)$ into the function $g(x)$ , replacing the $x$ -terms with the function $f(x)$ .

So, for $f(x)=\simplify{{m}x+{c}}$ and $g(x)=\simplify{{n}x+{d}}$ ,

$\begin{split} f \circ g(x) \equiv f(g(x)) &\,= \simplify{{m}({n}x+{d})+{c}} \\ &\,=\simplify[!collectNumbers,unitFactor]{{m*n}x+{m*d}+{c}} \\ &\,=\simplify{{m*n}x+{m*d+c}}, \end{split}$

and

$\begin{split} g \circ f(x) \equiv g(f(x)) &\,= \simplify{{n}({m}x+{c})+{d}} \\ &\,=\simplify[!collectNumbers,unitFactor]{{m*n}x+{n*c}+{d}} \\ &\,=\simplify{{m*n}x+{n*c+d}}. \end{split}$

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Christian Lawson-Perfect 2 years, 6 months ago

Ben McGovern 3 years, 9 months ago

Ben McGovern 4 years, 7 months ago

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Functions: Composite Functions 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ben McGovern 3 years, 9 months ago

Ben McGovern 4 years, 7 months ago

Error in variable testing condition

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Generated value: integer

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Generated value: `integer`