$f\left( x \right) = \left( {\frac{{{e^{2x}} - 1}}{{{e^{2x}} + 1}}} \right)$ is

JEE MATHEMATICS MCQ: INCREASING & DECREASING

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

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Correct option: A

An increasing

Option A (An increasing) is correct because the derivative of the function is positive for all x in R, indicating an increasing function.

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

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\left( { - \infty ,\;\infty } \right)