WBJEE · Maths · Continuity and Differentiability
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
- A \(f(2)=1\)
- B \(f(2)=2\)
- C \(f\) is continuous only at \(x=1\)
- D \(f\) is continuous at all points
Answer & Solution
Correct Answer
(C) \(f\) is continuous only at \(x=1\)
Step-by-step Solution
Detailed explanation
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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