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)

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.

  • 2
What are you looking for?