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If \(f(x)=\left\{\begin{array}{l}x ; \text { when } x \text { is rational } \\ 1-x ; \text { when } x \text { is irrational }\end{array}\right.\), then fof \((x)\) is given as
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Verified Answer
The correct answer is:
\(\mathrm{x}\)
\(\begin{aligned}
& f o f(x)=\left\{\begin{array}{l}
f(x) ; \text { when } f(x) \text { is rational } \\
1-f(x) \text {; when } f(x) \text { is irrational }
\end{array}\right. \\
& =\left\{\begin{array}{l}
\mathrm{x} ; \quad \text { when } \mathrm{x} \text { is rational } \\
1-(1-\mathrm{x}) ; \text { when } \mathrm{x} \text { is irrational }
\end{array}=\mathrm{x}\right. \\
&
\end{aligned}\)
& 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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