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Let $f: R \rightarrow R$ be such that $f(2 x-1)=f(x)$ for all $x \in R .$ If $f$ is continuous at $x=1$ an $f(1)=1,$ then
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The correct answers are:
$f$ is continuous only at $x=1$
Given, $f: R \rightarrow R$
and $\quad f(2 x-1)=f(x), x \in R$
Hence, $f$ is continuous at $x=1$ and $f(1)=1$
and $\quad f(2 x-1)=f(x), x \in R$
Hence, $f$ is continuous at $x=1$ and $f(1)=1$
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