Question

If $f\left(x\right)$ is a continuous function such that its value $\forall x\in R$ is a rational number and $f\left(1\right)+f\left(2\right)=6$ , then the value of $f\left(3\right)$ is equal to

• A. $3$
• B. $9$
• C. $2$
• D. $4$

Answer 1

Answer: (A)

Since $f\left(x\right)$ is continuous and attains only rational values, then by intermediate value theorem, $f\left(x\right)$ is a constant function.
i.e. $f\left(1\right)=f\left(2\right)=3$