Question

Let $f$ be a continuous function on [1,3]. lf $f$ takes only rational values for all $x$ and $f\left(2\right)=10$ then $f\left(1.5\right)$ is equal to

• A. $8$
• B. $\frac{f\left(1\right)+f\left(3\right)}{3}$
• C. $20$
• D. $10$

Answer 1

Answer: (D)

$10$

Since $f$ is continuous, so it must take all real values between $f\left(1\right)$ and $f\left(3\right)$.

But since $f$ takes only rational values so $f$ must be a constant function.

Hence $f\left(1.5\right)=f\left(2\right)=10$