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

Arun
25758 Points
2 years 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
2 years 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
2081 Points
2 years 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 :)