Question

Let $f:[-2,2]\to R$ be a continuous function such that $f\left(x\right)$ assumes only irrational values. If $f\left(\sqrt{2}\right)=\sqrt{2}$, then

• A. $f\left(0\right)=0$
• B. $f(\sqrt{2}-1)=\sqrt{2}-1$
• C. $f(\sqrt{2}-1)=\sqrt{2}+1$
• D. $f(\sqrt{2}-1)=\sqrt{2}$

Answer 1

The correct option is D $f(\sqrt{2}-1)=\sqrt{2}$

A continuous function assuming only irrational values must be a constant function.
i.e., $f\left(x\right)=\sqrt{2},\forall x\in R$