JEE Exam > JEE Videos > Mathematics (Maths) Class 12 > Invertible Functions
Invertible Functions Video Lecture | Mathematics (Maths) Class 12 - JEE
|
204 videos|290 docs|139 tests
|
FAQs on Invertible Functions Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What is an invertible function? |  |
Ans. An invertible function, also known as a one-to-one function, is a function that maps each element of its domain to a unique element in its range. In other words, for every input, there is exactly one output, and vice versa.
| 2. How can you determine if a function is invertible? | |
Ans. To determine if a function is invertible, you can use the horizontal line test. If no horizontal line intersects the graph of the function more than once, then the function is invertible. Additionally, a function must also be one-to-one, meaning that it passes the vertical line test, where no vertical line intersects the graph more than once.
| 3. What is the inverse of an invertible function? | |
Ans. The inverse of an invertible function is a new function that undoes the actions of the original function. In other words, if the original function maps an input x to an output y, then the inverse function maps y back to x. The inverse function is denoted as f^(-1)(x).
| 4. Can all functions be inverted? | |
Ans. No, not all functions can be inverted. Only functions that are one-to-one, or injective, can be inverted. If a function is not one-to-one, then there would be multiple inputs that map to the same output, making it impossible to determine the original input from the output.
| 5. How can you find the inverse of an invertible function? | |
Ans. To find the inverse of an invertible function, you can follow these steps:
1. Replace the function's notation with y.
2. Swap the roles of x and y in the equation.
3. Solve the equation for y to express it in terms of x.
4. Replace y with f^(-1)(x) to denote the inverse function.
5. Verify that the inverse function is indeed the inverse by using composition, where applying the original function and its inverse to an input should yield the original input.
Text Transcript from Video
convertible function let F be a function
from one to three to ABC and f is one
one and on to such that F of one is
equal to a F of two is equal to b f of 3
is equal to C there exists a function G
from ABC 2 1 2 3 touch that G of a is
equal to 1 G of B is equal to 2 G of C
is equal to 3 now let us examine G Oh F
and f or g between such functions let us
find geo F of 1 G of F 1 F of 1 is e and
g o f of a is equal to 1 so G or F of 1
is 1 similarly G oh F of 2 is 2 and G Oh
F of 3 is 3 it means do FX is equal to X
which is an identity function on X now
let us find f OG of a F or G of a is
equal to F of G a G of a is equal to 1
and F of 1 is equal to a similarly F or
G of B is B and F Oh G of C is C it
means f or g y is equal to y or it is an
identity function on Y it means function
f from X to Y is invertible if there
exists a function G from Y to X such
that G Oh F is equal to I X and F or G
is equal to I why function G is called
the inverse of function f and it is
denoted by F raised to the power minus 1
for a function to be invertible it must
be one one and onto or we can say if f
is one one and onto then f must be
invertible
from one to three to ABC and f is one
one and on to such that F of one is
equal to a F of two is equal to b f of 3
is equal to C there exists a function G
from ABC 2 1 2 3 touch that G of a is
equal to 1 G of B is equal to 2 G of C
is equal to 3 now let us examine G Oh F
and f or g between such functions let us
find geo F of 1 G of F 1 F of 1 is e and
g o f of a is equal to 1 so G or F of 1
is 1 similarly G oh F of 2 is 2 and G Oh
F of 3 is 3 it means do FX is equal to X
which is an identity function on X now
let us find f OG of a F or G of a is
equal to F of G a G of a is equal to 1
and F of 1 is equal to a similarly F or
G of B is B and F Oh G of C is C it
means f or g y is equal to y or it is an
identity function on Y it means function
f from X to Y is invertible if there
exists a function G from Y to X such
that G Oh F is equal to I X and F or G
is equal to I why function G is called
the inverse of function f and it is
denoted by F raised to the power minus 1
for a function to be invertible it must
be one one and onto or we can say if f
is one one and onto then f must be
invertible
About this Video
|
4.87/5 Rating |
|
Dec 22, 2024 Last updated |
Video Description: Invertible Functions for JEE 2024 is part of Mathematics (Maths) Class 12 preparation.
The notes and questions for Invertible Functions have been prepared according to the JEE exam syllabus.
Information about Invertible Functions covers all important topics for JEE 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Invertible Functions.
Introduction of Invertible Functions in English is available as part of our Mathematics (Maths) Class 12 for JEE & Invertible Functions in
Hindi for Mathematics (Maths) Class 12 course. Download more important topics related with notes, lectures and mock test series for
JEE Exam by signing up for free.
Description
Video Lecture & Questions for Invertible Functions Video Lecture | Mathematics (Maths) Class 12 - JEE - JEE full syllabus preparation | Free video for JEE exam to prepare for Mathematics (Maths) Class 12.
Information about Invertible Functions
Here you can find the meaning of Invertible Functions defined & explained in the simplest way possible.
Besides explaining types of Invertible Functions theory, EduRev gives you an ample number of questions to practice Invertible Functions tests,
examples and also practice JEE tests.
|
204 videos|290 docs|139 tests
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
MCQs
,Invertible Functions Video Lecture | Mathematics (Maths) Class 12 - JEE
,Extra Questions
,Important questions
,video lectures
,Previous Year Questions with Solutions
,practice quizzes
,shortcuts and tricks
,past year papers
,Free
,Sample Paper
,mock tests for examination
,Viva Questions
,ppt
,Semester Notes
,Summary
,Invertible Functions Video Lecture | Mathematics (Maths) Class 12 - JEE
,Exam
,study material
,Objective type Questions
,Invertible Functions Video Lecture | Mathematics (Maths) Class 12 - JEE
;
Study Invertible Functions on the App
Students of JEE can study Invertible Functions alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Invertible Functions,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Invertible Functions is prepared as per the latest JEE syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup