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RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS1 Mark
Question
Choose the correct answer from the given four options.
Let f : [0, 1] → [0, 1] be defined by $\text{f}(\text{x})=\begin{cases}\text{x, if x is rational}\\1-\text{x, if x is irrational}\end{cases}$ Then (fof)x is:
  1. constant
  2. 1 + x
  3. x
  4. none of these.
✓

Answer

  1. x

Solution:

We are given that, f : [0, 1] → [0, 1] be defined by $\text{f}(\text{x})=\begin{cases}\text{x, if x is rational}\\1-\text{x, if x is irrational}\end{cases}$

Now, $(\text{fof})\text{x} = \text{f}(\text{f(x)})$

$=\text{x}$

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