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JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

1 of 1

Analyzing +4 | -1

Let

f(x)

and

g(x)

be increasing and decreasing functions respectively from

[0, \infty)

to

[0, \infty)

, Let

h(x)=fog(x)

. If

h(0)=0

, then

h(x)

, is

View answer and explanation

Correct option: A

Always 0

Always 0. Since

h(x) = f(g(x))

,

f

is increasing, and

g

is decreasing,

h(x)

is decreasing. Given

h(0) = 0

and

h(x)

maps to

[0, \infty)

,

h(x)

must always be 0.

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If the function

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

is increasing for all values of

x

, then The set of values of a for which the function

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

is an increasing function on [1,2] is The value of

a

f(x)=

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

decreases for all real values is given by The function

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

f

g

are two increasing functions such that

fog

is defined, then If

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

0 < {b^2} < c

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