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Solution for The Function F(X) = Cot−1 X + X Increases in the Interval (A) (1, ∞) (B) (−1, ∞) (C) (−∞, ∞) (D) (0, ∞) - CBSE (Commerce) Class 12 - Mathematics

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Question

The function f(x) = cot−1 x + x increases in the interval
(a) (1, ∞)
(b) (−1, ∞)
(c) (−∞, ∞)
(d) (0, ∞)

Solution

(c) (−∞, ∞)

\[f\left( x \right) = \cot^{- 1} x + x\]

\[f'\left( x \right) = \frac{- 1}{1 + x^2} + 1\]

\[ = \frac{- 1 + 1 + x^2}{1 + x^2}\]

\[ = \frac{x^2}{1 + x^2} \geq 0, \forall x \in R\]

\[\text { So,f(x)is increasing on } \left( - \infty , \infty \right) .\]

  Is there an error in this question or solution?
Solution The Function F(X) = Cot−1 X + X Increases in the Interval (A) (1, ∞) (B) (−1, ∞) (C) (−∞, ∞) (D) (0, ∞) Concept: Increasing and Decreasing Functions.
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