Question

If [.] denote the greatest integer function then $f(x) = \frac{a^{x} + 1}{a^{x} - 1}$

$f(x) = x\left( \frac{a^{x} - 1}{a^{x} + 1} \right)$is –

• A. 0
• B. x
• C. x/2
• D. x²/2

Answer 1

Answer: (C)

x/2

Answer 2

nx – 1 < [nx] ≤ nx. Putting n = 1, 2, 3,…. , n and adding them,

x Σ n – n < Σ [nx] ≤ x Σ n

∴ x . – < ≤ x . … (1)

Now, = x . – =

As the two limits are equal, by (1)

= .

Hence (3) is correct answer.