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Let `A = R - {3}` and `B = R - {1}` . Consider the function `f: A- gt B` defined by `(x)=((x-2)/...
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Question From - NCERT Maths Class 12 Chapter 1 EXERCISE 1.2 Question – 10 RELATIONS AND FUNCTIONS CBSE, RBSE, UP, MP, BIHAR BOARD
QUESTION TEXT:-
Let `A = R - {3}` and `B = R - {1}` . Consider the function `f: A- gt B` defined by `(x)=((x-2)/(x-3))` . Is f one-one and onto? Justify your answer.
Doubtnut के साथ १००% मार्क्स पायें, आज ही डाउनलोड करें :-
Related Questions & Solutions:
1. Show that the functions `f: R_*- gt R_*` defined by `f(x)=1/x` is one-one and onto. where R* is the set of all non zero real numbers. Is the result true, if the domain R* is replaced by N with co-doma...
2. Check the injectivity and surjectivity of the following functions: (i) `f : N - gt N` given by `f(x)=x^2` (ii) `f : Z- gt Z` given by `f(x)=x^2` (iii) `f : R - gt R` given by `f(x)=x^2` (iv) `f : N- g...
3. Prove that the Greatest Integer Function `f : R- gt R ,` given by `f (x) = [x]` , is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x....
4. Show that the Modulus Function `f : R- gt R ,` given by `f (x) = | x |` , is neither one-one nor onto, where `| x |` is x, if x is positive or 0 and `| x |` is ` x` , if x is negative....
5. Show that the Signum Function `f : R- gt R ,` given by `f(x)={1,ifx gt 0 0,ifx=0-1, ifx lt 0` is neither one-one nor onto....
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QUESTION TEXT:-
Let `A = R - {3}` and `B = R - {1}` . Consider the function `f: A- gt B` defined by `(x)=((x-2)/(x-3))` . Is f one-one and onto? Justify your answer.
Doubtnut के साथ १००% मार्क्स पायें, आज ही डाउनलोड करें :-
Related Questions & Solutions:
1. Show that the functions `f: R_*- gt R_*` defined by `f(x)=1/x` is one-one and onto. where R* is the set of all non zero real numbers. Is the result true, if the domain R* is replaced by N with co-doma...
2. Check the injectivity and surjectivity of the following functions: (i) `f : N - gt N` given by `f(x)=x^2` (ii) `f : Z- gt Z` given by `f(x)=x^2` (iii) `f : R - gt R` given by `f(x)=x^2` (iv) `f : N- g...
3. Prove that the Greatest Integer Function `f : R- gt R ,` given by `f (x) = [x]` , is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x....
4. Show that the Modulus Function `f : R- gt R ,` given by `f (x) = | x |` , is neither one-one nor onto, where `| x |` is x, if x is positive or 0 and `| x |` is ` x` , if x is negative....
5. Show that the Signum Function `f : R- gt R ,` given by `f(x)={1,ifx gt 0 0,ifx=0-1, ifx lt 0` is neither one-one nor onto....
Get Classwise & Chapterwise Definitions & Solutions from NCERT Book:
Score 100% With Doubtnut
Prepare your class 12 subjects with our intuitive video solutions and score well in your final academic exam 2019-20. Students can click the doubt question from their text book of class 12 maths, physics, chemistry, biology, and find instant video solutions on our renowned doubt solving app or even on our website.
The video tutorials are helpful in preparation for the entrance exams like IIT JEE Main and Advanced, and NEET exam. Students can resolve their doubts with self-explanatory video solutions of questions from popular books of Math, Physics, Chemistry, Biology are solved for easy and swift learning.
Subscribe our channel for latest and trending videos on various topics from subjects like – Maths, Physics, Chemistry, Biology etc for Board & higher studies.
Doubtnut ऍप पर आप कक्षा ६ से १२ (IIT JEE तक) के NCERT के गणित/
भौतिक विज्ञान/रसायन विज्ञान/जीव विज्ञान/ के सभी सवालों के वीडियो देखिये और मुफ्त में खोजिये किसी
भी गणित सवाल का जवाब - 5 लाख से भी ज़्यादा सवालों के जवाब हैं Doubtnut ऍप पर
Doubtnut App and website has video solutions of ALL the NCERT questions from Class 6 to 12. You can download the NCERT solutions in pdf format too.
Doubtnut app provides free online video solutions that help students to better understand each topic and retain what they have learnt for a longer duration. It further helps in creating a stronger foundation for future classes.
You can also ask any question related to Math, Physics, Chemistry, Biology and get a video solution for FREE from a library of more than 5 Lakhs Videos
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