JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

f^{\prime}\left(x^2-4 x+3\right) > 0

for all

x \in (2,3)

, then

f(\sin x)

is increasing on

View answer and explanation

Correct option: A

\underset{n \in Z}{\cup} \in\left(2 n \pi,(4 n+1) \frac{\pi}{2}\right)

Option A (

\underset{{n \in Z}}{{\cup}} \in\left(2 n \pi,(4 n+1) \frac{{\pi}}{{2}}\right)

) is correct because

f(\sin x)

is increasing when

f'(\sin x) \cos x > 0

, which occurs on the given interval.

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f\left( x \right) = \frac{{K\sin x + 2\cos x}}{{\sin x + \cos x}}

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