Question

If $f\left(x\right)$ is continuous in [0, 1] and $f\left(x\right)=1$ for all rational numbers in [0, 1] then $f\left(\frac{1}{\sqrt{2}}\right)=1$.
If true enter 1 else enter 0

Answer 1

$f\left({\frac{1}{\sqrt{2}}}^{+}\right)=f\left({\frac{1}{\sqrt{2}}}^{-}\right)=f\left(\frac{1}{\sqrt{2}}\right)=1$ and $f\left(x\right)$ is continuous in $[0,1]$. Hence $f\left(\frac{1}{\sqrt{2}}\right)$ will also be 1.