Question

The function f (x) = tan 1x - x decreases in the interval
(A) (1,0)
(B) (-1,00)
(C) (-00,00)
(D) (0,00)​

Answer 1

Answer:

(-00,00) is the correct answer

Answer 2

$\: \: \boxed{\boxed{\sf{\mapsto \: Let \: us \: know \: the \: formula}}}$

$\large\mathsf \red{\frac{d}{dx} {tan}^{-1} x \: = \: \frac{1}{1+{x}^{2}}} \\ \\ \mathsf \red{given} \\ \\ \mathsf{f(x) \: = {tan}^{ - 1} x - x} \\ \\ \mathsf{{f}^{l}(x) \: = \: \frac{1}{1 + {x}^{2} } - 1 } \\ \\ \mathsf{ = \frac{1 - 1 - {x}^{2} }{1 + {x}^{2} } } \\ \\ \mathsf{{f}^{l}(x) \: = \: \frac{ - {x}^{2} }{1 + {x}^{2} } } \\ \\ \mathsf{{f}^{l}(x) < 0} \\ \\ \mathsf{ \mapsto \: {f}^{l}(x) = \frac{ - {x}^{2} }{1 + {x}^{2} } < 0 \: \: \: \: \forall \: x} \\ \\ x \in( - ∞, \: ∞)$

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