AP EAMCET · Maths · Functions
If a function \(f\) satisfies \(f(x+1)+f(x-1)=\sqrt{2} f(x)\), then \(f(x+2)+f(x-2)=\)
- A \(2 \cdot f(x)\)
- B \(f(x+1)-f(x-1)\)
- C \(4 \cdot f(x)\)
- D 0
Answer & Solution
Correct Answer
(D) 0
Step-by-step Solution
Detailed explanation
Given, \(f(x+1)+f(x-1)=\sqrt{2} f(x)\) ...(i) Replace \(x\) by \(x+1\) \(f(x+2)+f(x)=\sqrt{2} f(x+1)\) ...(ii) Replace \(x\) by \(x-1\) in Eq. (i), \(f(x)+f(x-2)=\sqrt{2} f(x-1)\) ...(iii) On adding Eqs. (ii) and (iii),…
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