JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Medium

1 of 1

Analyzing +4 | -1

Let

f(x)=e^{x}-x

and

g(x)=x^{2}-x, \forall x \in R

, then the set of all

x \in R

, where the function

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

is increasing is :

View answer and explanation

Correct option: D

\left[0, \frac{1}{2}\right] \cup[1, \infty)

Option D (

0, \frac{{1}}{{2}}

∪[1, ∞)) is correct because it represents the intervals where the derivative of h(x) is greater than or equal to zero, indicating an increasing function.

More Questions from INCREASING & DECREASING

Practice All Chapter MCQs →

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

in order that

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

, is If

f

and

g

are two increasing functions such that

fog

is defined, then If

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

and

0 < {b^2} < c

, then in

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