JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Medium

1 of 1

Analyzing +4 | -1

Consider the following two statements.

I: If

f(x)

and

g(x)

are continuous and monotonic functions on the real line

\mathbb{R}

, then

f(x)+g(x)

is also a monotonic function.

II: If

f(x)

is a continuous decreasing function for all

x>0

and

f(1)

is positive, then

f(x)=0

exactly at one value of

x

.
Then

View answer and explanation

Correct option: B

both I and II are false

Option B is correct because both statements I and II are false, as demonstrated by counterexamples.

More Questions from INCREASING & DECREASING

Practice All Chapter MCQs →

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)