Functions: Inverse Functions 2a

Error

There was an error loading the page.

Contributors

Ben McGovern

Feedback

From users who are members of MASH Bath: Question Bank :

Ben McGovern

said

Ready to use

3 years, 9 months ago

History

○

Christian Lawson-Perfect 2 years, 6 months ago

Published this.

○

Ben McGovern 3 years, 9 months ago

Gave some feedback: Ready to use

○

Ben McGovern 4 years, 6 months ago

Created this as a copy of Functions: Inverse Functions 1.

Name	Status	Author	Last Modified
Functions: Inverse Functions 1	Ready to use	Ben McGovern	10/10/2022 13:03
Functions: Inverse Functions 2a	Ready to use	Ben McGovern	10/10/2022 13:03
Functions: Inverse Functions 2b	Ready to use	Ben McGovern	10/10/2022 13:04
Functions: Inverse Functions 3	Ready to use	Ben McGovern	10/10/2022 13:04
Functions: Inverse Functions 4	Ready to use	Ben McGovern	10/10/2022 13:04
Functions: Inverse Functions 5	Ready to use	Ben McGovern	10/10/2022 13:04
CA6 Inverse functions	Ready to use	Megan Oliver	09/04/2024 15:42

There are 30 other versions that do you not have access to.

Question statement

If $f(x)=\simplify{({m}x+{c})/(x)}$ for $x\neq0$ , find the inverse function, $f^{-1}(x)$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

			m	integer	8
			c	integer	-5

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2..9)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0 Mathematical expression
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

$f^{-1}(x)=$ Gap 0

Advice

To find $f^{-1}x$ , it can help to first set $f(x)$ to a different variable, which we will call $y$ :

$y = f(x) = \simplify{({m}x+{c})/x}$

Since the function $f(x)$ takes us from $x$ to $y$ , the inverse function $f^{-1}$ will take us from $y$ to $x$ . So to obtain $f^{-1}$ , we want to rearrange $y=\simplify{({m}x+{c})/x}$ so that it is $x$ as a function of $y$ :

$\begin{split} y &\,= \simplify{({m}x+{c})/x} \\\\ \simplify{x*y} &\,= \simplify{{m}x+{c}} \\\\ \simplify{x*y-{m}x} &\,= \simplify{{c}} \\\\ \simplify{x(y-{m})} &\,= \simplify{{c}} \\\\ x&\,= \simplify{{c}/(y-{m})}. \end{split}$

Hence, $f^{-1}(y) =\simplify{{c}/(y-{m})}$ , and therefore

$f^{-1}(x) =\simplify{{c}/(x-{m})}.$

(Note: The inverse is valid for all values of $x$ except $x=\var{m}$ , since this would make the denominator equal to 0.)

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet

This question is used in the following exams:

Inverse Functions by Ben McGovern in MASH Bath: Moodle quizzes and TS.
All the good stuff by Chris Templet in Chris's workspace.
Inverse Functions by Julie Crowley in Julie's workspace.
CETL-MSOR 2023 Workshop by Ben McGovern in Ben's workspace.
W4 2324 by Jose Camarena Brenes in EMSE.

Loading...

Error

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, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

Error

Functions: Inverse Functions 2a

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, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`