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BITSAT 2011
Exam
BITSAT
Year
2011
Subject
Mathematics
Chapter
Functions

BITSAT 2011 · Mathematics · Functions

If (f(x)=\ array l x ; when x is rational 1-x ; when x is...

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

Options

  1. A1
  2. B(\mathrm{x})
  3. C(1+\mathrm{x})
  4. DNone of these

Correct answer

B. (\mathrm{x})

Step-by-step solution

(fof(x)={f(x); when f(x) is rational 1−f(x); when f(x) is irrational ={x; when x is rational 1−(1−x); when x is irrational =x\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})
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