Let $‘f’$ be a continuity function on $\left[1,3\right].$ If $‘f’$ takes only rational values for $‘x’$ and $f\left(2\right)=10$ then $f\left(1.5\right)=$

$f$ is continuous on $\left[1,3\right]$ 

Given $f\left(x\right)$ can takes only  Rational values $\forall x$

Given $f\left(2\right)=10$

if f(x) takes any rational number other than 10 say ‘n’ then it should take the irrational values between 10 and n which contradicts the statement. hence

$\Rightarrow f\left(x\right)$ is constant function, $f\left(x\right)=10,\forall x\in [1,3]$

$\Rightarrow f\left(1.5\right)=10$