Question

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

• A. 4
• B. 1
• C. 2
• D. 0

Answer 1

Answer: (A)

$f(x)=2+\frac{4}{\pi }\left(\pi -{\cot }^{-1}(-x)\right)-\frac{\pi }{4{\cot }^{-1}(-x)}\left[\Theta {\cot }^{-1}(x)>0\right]$
$=2+4-\left[\frac{4}{\pi }{\cot }^{-1}(-x)+\frac{\pi }{4{\cot }^{-1}(-x)}\right]$
$\le 2+4-2=4$
$f(x{)}_{\max }=4$