If: R → R be defines as follows: f(x)= 1 ∈ Q, f(x)= -1 x ∉ Q (i)f ( 1/2 ) , f(π)

Question

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 1

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

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