WBJEE · Maths · Functions
If \(f(x)=x\left(\frac{1}{x-1}+\frac{1}{x}+\frac{1}{x+1}\right), x>1\). Then
- A \(f(x) \leq 1\)
- B \(1 < f(x) \leq 2\)
- C \(2 < f(x) \leq 3\)
- D \(f(x)>3\)
Answer & Solution
Correct Answer
(D) \(f(x)>3\)
Step-by-step Solution
Detailed explanation
Given function is \[ \begin{aligned} f(x) &=x\left\{\frac{1}{x-1}+\frac{1}{x}+\frac{1}{x+1}\right\}, x>1 \\ &=x\left\{\frac{2 x}{x^{2}-1}+\frac{1}{x}\right\}=\frac{2 x^{2}}{x^{2}-1}+1 \\ &=\left\{\frac{2}{\left(1-\frac{1}{x^{2}}\right)}+1\right\}>3 \end{aligned} \]…
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