Functions: Composite Functions 4b

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Christian Lawson-Perfect 2 years, 6 months ago

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Created this as a copy of Functions: Composite Functions 3b.

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 $f(x)=\simplify{{a}x^2+{m}x+{c}}$ and $g(x)=\simplify{e^({k}x)}$ , 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

k	integer	2
m	integer	3
c	integer	7
a	integer	2
advice	string	<p>\[ g \circ f(x) \equiv g(f(
simp	number	1
sol1	string	<p>\[ g \circ f(x) \equiv g(f(
sol2	string	<p>\[ \begin{split} g \circ f(

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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 $f(x)=\simplify{{a}x^2+{m}x+{c}}$ and $g(x)=\simplify{e^({k}x)}$ ,

$\begin{split} f \circ g(x) \equiv f(g(x)) &\,= \simplify[unitFactor]{{a}*[e^({k}x)]^2+{m}(e^({k}x))+{c}} \\ &\,= \simplify{{a}e^({2k}x)+{m}e^({k}x)+{c}}, \end{split}$

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{advice}

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This question is used in the following exams:

All the good stuff by Chris Templet in Chris's workspace.
Composite Functions by Ben McGovern in MASH Bath: Moodle quizzes and TS.
EGD125_Quiz1 by Matt Falk in Matt's workspace.

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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 4b

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`