JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

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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 function

h(x) = (fog)(x)

is increasing, is

View answer and explanation

Correct option: A

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

Option A (

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

) 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

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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

g

fog

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

0 < {b^2} < c

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