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Question: Answered & Verified by Expert
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
MathematicsContinuity and DifferentiabilityWBJEEWBJEE 2015
Options:
  • A $f(2)=1$
  • B $f(2)=2$
  • C $f$ is continuous only at $x=1$
  • D $f$ is continuous at all points
Solution:
1644 Upvotes Verified Answer
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 $f(1)=1$

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