Question

Let $f:R\to Z$ be a continuous function such that $f\left(9\right)=3.$ Then the value of $f\left(25\right)-f\left(1\right)$ is

• A. $4$
• B. $3$
• C. cannot be determined
• D. $0$

Answer 1

The correct option is D $0$

As $f$ is continuous in $R$ and can give only integral value, so $f\left(x\right)$ is a constant function.
$f\left(x\right)=p$ (say)
As $f\left(9\right)=3$, so
$f\left(x\right)=3$
$\therefore f\left(25\right)-f\left(1\right)=0$