Question

If f(x) = $\left\{ \begin{aligned} & x ⥄ ⥄ when ⥄ ⥄ x ⥄ ⥄ is ⥄ rational \\ & 1 - x ⥄ when ⥄ x ⥄ is ⥄ ⥄ irrational ⥄ \end{aligned} \right.\$, then of (x) is given as

• A. 1
• B. x
• C. 1 + x
• D. None of these

Answer 1

Answer: (B)

x

Answer 2

fof(x) = $\left\{ \begin{aligned} & f(x)whenf(x)isrational \\ & 1 - f(x)whenf(x)isirrational \end{aligned} \right.\$

= $\left\{ \begin{aligned} & xwhenxisrational \\ & 1 - (1 - x)whenxisirrational \end{aligned} \right.\$= x