Choose the correct answer from the given four options. Let f : [0… - Vidyadip

MCQ

Choose the correct answer from the given four options.
Let $f : [0, 1] \rightarrow [0, 1]$ 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 $\text{(fof)x}$ is:

A
constant
B
$1 + x$
✓
$x$
D
none of these.

✓

Answer

Correct option: C.

$x$

We are given that$, f : [0, 1] \rightarrow [0, 1]$ 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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