Ask Questions, Get Answers
Menu
X
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
5 Test Series
CBSE XII
Math
JEEMAIN
Math
Physics
Chemistry
Practice Test Series
CBSE XI
Math
NEET
Physics
Chemistry
Biology - XII
Biology - XI
Olympiad class V
Math - 5 Test Series
Olympiad class VI
Math - 5 Test Series
studyplans
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
5 Test Series
CBSE XII
Math
JEEMAIN
Math
Physics
Chemistry
Practice Test Series
CBSE XI
Math
NEET
Physics
Chemistry
Biology - XII
Biology - XI
Olympiad class V
Math - 5 Test Series
Olympiad class VI
Math - 5 Test Series
mobile
exams
ask
sample papers
tutors
pricing
sign-in
Download our FREE mobile app with 1000+ tests for CBSE, JEE MAIN, NEET
X
Search
Topics
Want to ask us a question?
Click here
Browse Questions
Student Questions
Ad
Home
>>
CBSE XII
>>
Math
>>
Relations and Functions
0
votes
State with reason whether following functions have inverses: (i) \( f: \{ 1,2,3,4,\} \to \{10\}\) with \( f= \{(1,10),(2,10),(3,10), (4,10)\}\)
This is part of a multipart question and answered separately here on Clay6.com
class12
cbse
ch1
sec3
q5
q5-1
easy
sec-a
p18
math
Share
asked
Mar 19, 2013
by
balaji.thirumalai
Please
log in
or
register
to add a comment.
Can you answer this question?
Do not ask me again to answer questions
Please
log in
or
register
to answer this question.
1 Answer
0
votes
Toolbox:
To check if a function is invertible or not ,we see if the function is both one-one and onto.
A function $f: A \rightarrow B$ where for every $x1, x2 \in X, f(x1) = f(x2) \Rightarrow x1 = x2$ is called a one-one or injective function.
A function$ f : X \rightarrow Y$ is said to be onto or surjective, if every element of Y is the image of some element of X under f, i.e., for every $y \in Y$, there exists an element x in X such that $f(x) = y$.
Given $f:\{1,2,3,4\} \to \{10\}$ with $f=\{(1,10),(2,10,(3,10)(4,10)\}$
Step 1: Checking for one-one:
From the given definition of $f$, we can see that it is many-one, as for every ${1,2,3,4} \in f, f(1) = f(2) = f(3) = f(4) = 10$.
Therfore, the function does not have an inverse. We don't need to check further for onto.
answered
Mar 19, 2013
by
balaji.thirumalai
State with reason whether following functions have inverse: (ii) \(g: \{ 5,6,7,8\} \to \{1,2,3,4\}\) with \(g= \{(5,4),(6,3),(7,4),(8,2)\}\)
True or False: The function $f$ has an inverse: $ f:{1,2,3,4,}\to{10}$ with $f={(1,10),(2,10),(3,10),(4,10)}$
Please
log in
or
register
to add a comment.
Related questions
0
votes
1
answer
State with reason whether following functions have inverse: (iii) \(h: \{2,3,4,5,\} \to \{7,9,11,13\}\) with \(h=\{(2,7),(3,9),(4,11),(5,13) \} \)
asked
Nov 9, 2012
by
vaishali.a
cbse
class12
bookproblem
ch1
sec3
q5
p18
q5-3
sec-a
easy
math
0
votes
1
answer
State with reason whether following functions have inverse: (ii) \(g: \{ 5,6,7,8\} \to \{1,2,3,4\}\) with \(g= \{(5,4),(6,3),(7,4),(8,2)\}\)
asked
Mar 19, 2013
by
balaji.thirumalai
cbse
class12
ch1
sec3
p18
sec-a
bookproblem
q5
q5-2
math
0
votes
1
answer
Let \(f,\, g\, and\, h\) be functions from \(R\, to\, R.\) Show that \[ (f+g) oh = foh + goh\]
asked
Nov 9, 2012
by
vaishali.a
cbse
class12
bookproblem
ch1
sec3
q2
p18
easy
sec-a
q2-1
math
0
votes
1
answer
Find \( gof\) and \(fog\), if (i) \( f(x) = |\;x\;| \, and \, g(x) = |\;5x-2\;| \)
asked
Nov 9, 2012
by
vaishali.a
cbse
class12
bookproblem
ch1
sec3
q3
q3-1
p18
easy
sec-a
math
0
votes
1
answer
For the matrices $A$ and $B$, verify that $(AB)' = B'A'$ , where $$ \text{ (i) } A = \begin{bmatrix} 1 \\ -4 \\ 3 \end{bmatrix} \text{ , } B = \begin{bmatrix} -1 & 2 & 1 \end{bmatrix} \qquad $$
asked
Nov 25, 2012
by
pady_1
cbse
class12
bookproblem
ch3
sec3
q5
p88
easy
q5-1
sec-b
math
0
votes
1
answer
Let \(f:\{1,3,4\} \to \{1,2,5\}and\;g:\{1,2,5\}\to\{1,3\}\) be given by \(f = \{(1, 2), (3, 5), (4, 1)\} \;and\; g = \{(1, 3), (2, 3), (5, 1)\}\). Write down \(gof\).
asked
Nov 9, 2012
by
vaishali.a
cbse
class12
bookproblem
ch1
sec3
q1
p18
easy
sec-a
math
0
votes
1
answer
Consider \( f:R_+ \to [4,\infty)\)given by \(f(x)=x^2 +4\). Show that \(f\) is invertible with the inverse \(f^{-1}\)of \(f\) given by \(f^{-1}(y) = \sqrt {y-4}\),where $R_+$ is the set of all non-negative real numbers.
asked
Nov 14, 2012
by
vaishali.a
cbse
class12
bookproblem
ch1
sec3
q8
p18
medium
sec-b
math
Ask Question
Tag:
Math
Phy
Chem
Bio
Other
SUBMIT QUESTION
►
Please Wait
Take Test
JEEMAIN Crash Practice
15 Test Series
NEET Crash Practice
5 Test Series
JEEMAIN
350+ TESTS
NEET
320+ TESTS
CBSE XI MATH
50+ TESTS
CBSE XII MATH
80+ TESTS
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...