If: R → R be defines as follows: \( f(x) = \begin{cases} 1 & \quad

1.	If: R → R be defines as follows: \( f(x) = \begin{cases} 1 & \quad x\in Q\\ -1 & \quad x \notin Q \end{cases}\) Find f \((\frac{1}{2})\) , \(f(\pi)\)
Answer» The value of the function for every rational number is 1 and for every irrational number is – 1 \(\quad \therefore \frac{1}{2}\in Q \implies f(\frac{1}{2})=1 \quad\\\text{ And }\quad \pi \notin \text {Q }\implies f(\pi) = -1 \)

If: R → R be defines as follows: \( f(x) = \begin{cases} 1 & \quad x\in Q\\ -1 & \quad x \notin Q \end{cases}\) Find f \((\frac{1}{2})\) , \(f(\pi)\)

Answer»

The value of the function for every rational number is 1 and for every irrational number is – 1

\(\quad \therefore \frac{1}{2}\in Q \implies f(\frac{1}{2})=1 \quad\\\text{ And }\quad \pi \notin \text {Q }\implies f(\pi) = -1 \)