JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

1 of 1

Analyzing +4 | -1

Let the function

g:(-\infty, \infty) \rightarrow(-\pi / 2, \pi / 2)

be given by

g(u)=2 \tan ^{-1}\left(e^{u }\right)-\frac{\pi}{2}

. Then,

g

View answer and explanation

Correct option: C

Odd and is strictly increasing in

(-\infty, \infty)

The correct answer is C (Odd and is strictly increasing in

(-\infty, \infty)

) because the derivative

g'(u)

is always positive, indicating that

g(u)

is strictly increasing, and

g(-u) = -g(u)

, showing that

g(u)

is odd.

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

x

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a

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\sin x-\cos x-a x+b

f(x)=x e^{x(1-x)}, x \in R

f

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fog

f\left( x \right) = {x^3} + b{x^2} + cx + d

0 < {b^2} < c

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