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Grade: 12th pass

                        

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

one year ago

Answers : (3)

Arun
25359 Points
							
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.
 
 
one year ago
Vikas TU
13783 Points
							
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 
one year ago
Aditya Gupta
2069 Points
							
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 :)
one year ago
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