WBJEE · Maths · Functions
Let \(f:[-2,2] \rightarrow R\) be a continuous function such that \(f(x)\) assumes only irrational values. If \(f(\sqrt{2})=\sqrt{2},\) then
- A \(f(0)=0\)
- B \(f(\sqrt{2}-1)=\sqrt{2}-1\)
- C \(f(\sqrt{2}-1)=\sqrt{2}+1\)
- D \(f(\sqrt{2}-1)=\sqrt{2}\)
Answer & Solution
Correct Answer
(D) \(f(\sqrt{2}-1)=\sqrt{2}\)
Step-by-step Solution
Detailed explanation
If a function \(f(x)\) assumes only irrational values which is also continuous, then \(f(x)\) must be constant function. \(\Rightarrow \quad f(x)=\sqrt{2}\) \[ [\because f(\sqrt{2})=\sqrt{2} \mid \] \(\therefore \quad f(\sqrt{2}-1)=\sqrt{2}\)
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