WBJEE · Maths · Sequences and Series
Let \(f(x)=x+1 / 2\). Then, the number of real values of \(x\) for which the three unequal terms \(f(x), f(2 x), f(4 x)\) are in \(\mathrm{HP}\) is
- A 1
- B 0
- C 3
- D 2
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
Given, \(f(x)=x+\frac{1}{2}=\frac{2 x+1}{2}\) \(\therefore\) \(f(2 x)=2 x+\frac{1}{2}\) \(\Rightarrow\) \(f(2 x)=\frac{4 x+1}{2}\) and \(f(4 x)=4 x+\frac{1}{2} \Rightarrow f(4 x)=\frac{8 x+1}{2}\) since, \(f(x), f(2 x)\) and \(f(4 x)\) are in \(\mathrm{HP}\).…
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