If f (x) = \frac{4}{\pi} \left(cot\right)^{- 1} x - \frac{\pi}{4 \left(cot\right)^{- 1} \left(\right. - x \left.\right)} + 2 , then the maximum admissible value of f (x) will be

Engineering

Mathematics

Properties of Inverse Trigonometric Function

Question

If f (x) = $\frac{4}{π} \cot^{- 1} x - \frac{π}{4 \cot^{- 1} (- x)} + 2,$ then the maximum admissible value of f (x) will be

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$f (x) = 2 + \frac{4}{π} (π - \cot^{- 1} (- x)) - \frac{π}{4 \cot^{- 1} (- x)}$ [ $∵$ cot^–1(x) > 0]

$= 2 + 4 - [\frac{4}{π} \cot^{- 1} (- x) + \frac{π}{4 \cot^{- 1} (- x)}]$

$\leq$ 2 + 4 – 2 = 4

f (x)_max. = 4