AP EAMCET · Maths · Functions
Let \(Q\) be the set of all rational numbers in \([0,1]\) and \(f:[0,1] \rightarrow[0,1]\) be defined by
\[
f(x)=\left\{\begin{array}{r}
x \text { for } x \in Q \\
1-x \text { for } x \notin Q
\end{array}\right.
\]
Then, the set \(S=\{x \in[0,21]:(f o f)(x)\}\) is equal to
- A \([0,1]\)
- B \(-Q\)
- C \([0,1]-Q\)
- D \((0,1)\)
Answer & Solution
Correct Answer
(A) \([0,1]\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=\left\{\begin{array}{cc}x & \text { for } x \in Q \\ 1-x & \text { for } x \notin Q\end{array}\right.\) is defined for \[ f:[0,1] \rightarrow[0,1] \] If \(x\) is rational, then \[ \begin{array}{rlrl} f(x) & =x \\ \therefore \quad & f(f(x)) & =f(x)=x \end{array} \]…
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