JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

1 of 1

Analyzing +4 | -1

f

and

g

are two increasing functions such that

fog

is defined, then

View answer and explanation

Correct option: A

gof

is an increasing function

Option A (

gof

is an increasing function) is correct because the composition of two increasing functions is also an increasing function.

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

x

f\left( x \right) = {x^2} + ax + 1

a

f(x)=

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

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

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

0 < {b^2} < c

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

g:\,(0,\infty ) \to R

\int {\left( {\frac{{x(\cos x - \sin x)}}{{{e^x} + 1}} + \frac{{g(x)\left( {{e^x} + 1 - x{e^x}} \right)}}{{{{\left( {{e^x} + 1} \right)}^2}}}} \right)} dx = \frac{{xg(x)}}{{{e^x} + 1}} + c

x > 0,

c