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Question number 3........................... ...........

Question number 3...........................      ........... 

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Grade:12th pass

3 Answers

25763 Points
one year ago
Dear student
As it is said that f is continuous function hence f(10) can take any value irrespective of given options. Hence can't be determined.
Vikas TU
14149 Points
one year ago
Dear student 
The domain of function is defined only from 1 to 10 , And the function is continuous , So , The Range of function will only come from 1 to 10 . 
Hope this will help 
Good Luck 
Aditya Gupta
2075 Points
one year ago
hello sanjay, both the above answers are wrong. the correct answer would be option 2 f(10)= 10.
in fact, f(x)= 10 for all x in [1, 10].
reason: note that f is defined from [1, 10] to Q. but Q stands for rational numbers. now, lets assume there exists an x= m in [1, 10] for which f(m) is not equal to 10. then, by intermediate value theorem it would mean that f takes all the possible values between f(m) and 10 as f is continuous. however, given any two distinct real numbers, there always exist infinitely many rational as well as irrational numbers between them. so, it means that since f(m) and 10 are distinct, f is bound to have attained an irrational value lying in between  f(m) and 10. but f could have only attained rational values, hence by contradiction our initial claim that there exists an x= m in [1, 10] for which f(m) is not equal to 10 was FALSE. so, f(x)= 10.
kindly approve :)

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