Let f(x) be a continuous function defined for 1≤x≤3.  If f(x) takes rational values for all x and f(2)=10.  Then the value of f(1.5) is

As f(x) is continuous in [1,  3], f(x)  will attain all values between f(1)  and f(3).  As f(x)  takes rational values for allx and there are innumerable irrational values between f(1)  and f(3) which implies thatf(x)  can take rational values for all x  if f(x)  has a constant values at all points between x=1 and x=3.