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If $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{ll}1 & \mathrm{x} \text { is a rational number } \\ 0, & \mathrm{x} \text { is an irrational number, }\end{array}\right.$ what is/are the value(s) of (f of) $(\sqrt{3)}$ ?
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The correct answer is:
1
From the given direction of function
$\mathrm{f}(\mathrm{x})=\left\{\begin{array}{ll}1, & \mathrm{x} \text { is a rational number } \\ 0, & \mathrm{x} \text { is an irrational number }\end{array}\right.$
$($ f 0 f $) \sqrt{3}=\mathrm{f}\{\mathrm{f}(\sqrt{3})\}$
$=\mathrm{f}(0) \quad(\because \sqrt{3}$ is an irrational number $)$ $=1$
$(\because 0$ is a rational number)
$\mathrm{f}(\mathrm{x})=\left\{\begin{array}{ll}1, & \mathrm{x} \text { is a rational number } \\ 0, & \mathrm{x} \text { is an irrational number }\end{array}\right.$
$($ f 0 f $) \sqrt{3}=\mathrm{f}\{\mathrm{f}(\sqrt{3})\}$
$=\mathrm{f}(0) \quad(\because \sqrt{3}$ is an irrational number $)$ $=1$
$(\because 0$ is a rational number)
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