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
True or False: The function $f$ has an inverse: $ f:{1,2,3,4,}\to{10}$ with $f={(1,10),(2,10),(3,10),(4,10)}$
related to an answer for:
State with reason whether following functions have inverses: (i) \( f: \{ 1,2,3,4,\} \to \{10\}\) with \( f= \{(1,10),(2,10),(3,10), (4,10)\}\)
cbse
class12
additionalproblem
ch1
easy
sec-a
math
Share
asked
Mar 19, 2013
by
balaji.thirumalai
edited
Dec 5, 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.
Answer: False.
answered
Mar 19, 2013
by
balaji.thirumalai
Please
log in
or
register
to add a comment.
Related questions
0
votes
1
answer
True or False: If a function $f: X \rightarrow Y$ is invertible, it has a unique inverse.
asked
Mar 19, 2013
by
balaji.thirumalai
cbse
class12
ch1
toolbox
concepts
true-or-false
sec-a
easy
math
0
votes
1
answer
The following function $h: \{2,3,4,5,\} \to \{7,9,11,13\}$ with $ h=\{(2,7),(3,9),(4,11),(5,13) \}$ is invertible. True or False?
asked
Mar 19, 2013
by
balaji.thirumalai
cbse
class12
ch1
short-answer
additionalproblem
sec-a
math
0
votes
1
answer
Let \(f : X \to Y\) be an invertible function. Show that the inverse of $f^{-1}$ is $f$, i.e., $(f^{-1})^{-1} = f$.
asked
Nov 16, 2012
by
vaishali.a
cbse
class12
bookproblem
ch1
sec3
q12
p19
easy
sec-a
math
0
votes
1
answer
The function $g: \{ 5,6,7,8\} \to \{1,2,3,4\}$ is invertible. True or False?
asked
Mar 19, 2013
by
balaji.thirumalai
class12
cbse
ch1
additionalproblem
easy
sec-a
math
0
votes
1
answer
Given the Modulus Function \(f : R \to R\), given by \( f(x) = |\;x\;|\), where\( |\;x\;|\; is\; x\), if \(x\) is positive or \(0\) and \(|\;x\;|\; is\; \) \(-\)\(x\), if \( x\) is negative. Is $f$ one-one or onto?
asked
Mar 13, 2013
by
balaji.thirumalai
cbse
class12
ch1
sec2
sec-a
additionalproblem
easy
math
0
votes
1
answer
True or False: Let $f:R \rightarrow R$ be the function defined by f(x)=sin (3x+2)$\quad x\in R$.Then f is invertible.
asked
Dec 20, 2012
by
sreemathi.v
cbse
class12
ch1
q54
p17
true-or-false
exemplar
math
sec-a
0
votes
1
answer
Given the Function $f:R\rightarrow R$, given by $f(x)=[x]$, where $[x]$ denotes the greatest integer less than or equal to $x$ which of the following is true?
asked
Mar 13, 2013
by
balaji.thirumalai
cbse
class12
ch1
sec2
additionalproblem
easy
sec-a
math
Ask Question
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
...