let f be continuous function on [1,3] If f takes only rational values for all x and f(2)=1- , - Maths - Relations and Functions

Question

let f be continuous function on [1,3] If f takes only rational
values for all x and f(2)=1- , find f(1 5)

Vipin Verma · Accepted Answer

As f(x) is continuous and takes all the rational values from [
1,3]
Therefore f(x) must be constant function , as between two rational
numbers there exist infinite number of irrational numbers , so if
f(x) is not constant , then it cannot be continuous

So as f(2) = 1 , so f(1 5) will also be 1

let f be continuous function on [1,3]. If f takes only rational values for all x and f(2)=1- , find f(1.5)