>
Exams
>
Mathematics
>
Continuity and differentiability
>
the set of all points where the function f x x 1 x
Question:
The set of all points, where the function
f
(
x
)
=
x
(
1
+
∣
x
∣
)
f(x)=\frac{x}{(1+|x|)}
f
(
x
)
=
(
1
+
∣
x
∣
)
x
is differentiable, is
CUET (PG) - 2023
CUET (PG)
Updated On:
Mar 12, 2025
(0,∞)
(-∞,∞)
(-∞,0)U(0,∞)
[-1,0]
Hide Solution
Verified By Collegedunia
The Correct Option is
B
Solution and Explanation
The correct option is(B):(-∞,∞)
Download Solution in PDF
Was this answer helpful?
0
0
Top Questions on Continuity and differentiability
Let
f
:
R
→
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
→
R
be a twice-differentiable function such that
f
(
2
)
=
1
f(2) = 1
f
(
2
)
=
1
. If
F
(
x
)
=
x
f
(
x
)
F(x) = x f(x)
F
(
x
)
=
x
f
(
x
)
for all
x
∈
R
x \in \mathbb{R}
x
∈
R
, and the integrals
∫
0
2
x
F
′
(
x
)
d
x
=
6
\int_0^2 x F'(x) \, dx = 6
∫
0
2
x
F
′
(
x
)
d
x
=
6
and
∫
0
2
x
2
F
′
′
(
x
)
d
x
=
40
\int_0^2 x^2 F''(x) \, dx = 40
∫
0
2
x
2
F
′′
(
x
)
d
x
=
40
, then
F
′
(
2
)
+
∫
0
2
F
(
x
)
d
x
F'(2) + \int_0^2 F(x) \, dx
F
′
(
2
)
+
∫
0
2
F
(
x
)
d
x
is equal to:
JEE Main - 2025
Mathematics
Continuity and differentiability
View Solution
If
f
(
x
)
=
∫
1
x
1
/
4
(
1
+
x
1
/
4
)
d
x
,
f
(
0
)
=
−
6
,
t
h
e
n
f
(
1
)
i
s
e
q
u
a
l
t
o
:
f(x) = \int \frac{1}{x^{1/4} (1 + x^{1/4})} \, dx, \quad f(0) = -6, { then } f(1) { is equal to:}
f
(
x
)
=
∫
x
1/4
(
1
+
x
1/4
)
1
d
x
,
f
(
0
)
=
−
6
,
t
h
e
n
f
(
1
)
i
se
q
u
a
lt
o
:
JEE Main - 2025
Mathematics
Continuity and differentiability
View Solution
Let [x] denote the greatest integer function. Then match List-I with List-II:
CUET (UG) - 2024
Mathematics
Continuity and differentiability
View Solution
If
f
(
x
)
,
defined by
f
(
x
)
=
{
k
x
+
1
if
x
≤
π
cos
x
if
x
>
π
is continuous at
x
=
π
,
then the value of
k
is:
\text{ If } f(x), \text{ defined by } f(x) = \begin{cases} kx + 1 & \text{if } x \leq \pi \\ \cos x & \text{if } x > \pi \end{cases} \text{ is continuous at } x = \pi, \text{ then the value of } k \text{ is:}
If
f
(
x
)
,
defined by
f
(
x
)
=
{
k
x
+
1
cos
x
if
x
≤
π
if
x
>
π
is continuous at
x
=
π
,
then the value of
k
is:
CUET (UG) - 2024
Mathematics
Continuity and differentiability
View Solution
Let
f
:
R
→
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
→
R
be a function given by
f
(
x
)
=
{
1
−
cos
2
x
x
2
,
x
<
0
α
,
x
=
0
,
where
α
,
β
∈
R
.
β
1
−
cos
x
/
x
,
x
>
0
f(x) = \begin{cases} \frac{1 - \cos 2x}{x^2}, & x < 0 \\\alpha, & x = 0, \text{ where } \alpha, \beta \in \mathbb{R}. \\\beta \sqrt{1 - \cos x} / x, & x > 0 \end{cases}
f
(
x
)
=
⎩
⎨
⎧
x
2
1
−
c
o
s
2
x
,
α
,
β
1
−
cos
x
/
x
,
x
<
0
x
=
0
,
where
α
,
β
∈
R
.
x
>
0
If
f
f
f
is continuous at
x
=
0
x = 0
x
=
0
, then
α
2
+
β
2
\alpha^2 + \beta^2
α
2
+
β
2
is equal to:
JEE Main - 2024
Mathematics
Continuity and differentiability
View Solution
View More Questions
Questions Asked in CUET PG exam
What is the correct verb form: He, as well as his friends, ?
CUET (PG) - 2025
Verbs
View Solution
Which preposition is correct: Chanakya lived ?
CUET (PG) - 2025
Prepositions
View Solution
Identify the possessive noun: My office car is parked elsewhere.
CUET (PG) - 2025
Nouns
View Solution
Which tense is appropriate: How did Saira ?
CUET (PG) - 2025
Tenses
View Solution
Complete the sentence: There is a growing synthesis between humanism and ?
CUET (PG) - 2025
Sentence Completion
View Solution
View More Questions