Q65 / 125 · BITSAT 2011 · Mathematics

If \(f(x)=\left\{\begin{array}{l}x ; \text { when } x \text { is rational } \\ 1-x ; \text { when } x \text { is irrational }\end{array}\right.\), then fof \((x)\) is given as

  • A
    1
  • Correct answer
    B
    \(\mathrm{x}\)
  • C
    \(1+\mathrm{x}\)
  • D
    None of these

Solution

\(\begin{aligned} & f o f(x)=\left\{\begin{array}{l} f(x) ; \text { when } f(x) \text { is rational } \\ 1-f(x) \text {; when } f(x) \text { is irrational } \end{array}\right. \\ & =\left\{\begin{array}{l} \mathrm{x} ; \quad \text { when } \mathrm{x} \text { is rational } \\ 1-(1-\mathrm{x}) ; \text { when } \mathrm{x} \text { is irrational } \end{array}=\mathrm{x}\right. \\ & \end{aligned}\)

Hence, the correct answer is option: 'B'.

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