1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Even Extension of a Function
Let fx=x+|x-1...
Question
Let
f
(
x
)
=
x
+
|
x
−
100
|
−
|
x
+
100
|
and
g
(
x
)
=
|
f
(
x
)
|
−
1
,
then
A
f
(
x
)
is neither even nor odd
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
g
(
x
)
=
0
has
6
solutions
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
g
(
x
)
is an even function
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
f
(
x
)
is an odd function
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution
The correct option is
D
f
(
x
)
is an odd function
f
(
x
)
=
x
+
|
x
−
100
|
−
|
x
+
100
|
⇒
f
(
x
)
=
⎧
⎨
⎩
200
+
x
;
x
<
−
100
−
x
;
−
100
≤
x
≤
100
x
−
200
;
x
>
100
Graph of
f
(
x
)
Clearly,
f
(
x
)
is an odd function.
Now,
g
(
x
)
=
|
f
(
x
)
|
−
1
Graph of
|
f
(
x
)
|
is
Graph of
g
(
x
)
is
It can be observed that
g
(
x
)
is symmetrical with respect to
y
−
axis. So
g
(
x
)
is even function.
Therefore,
g
(
x
)
=
0
has
6
solutions
Suggest Corrections
0
Similar questions
Q.
Find fog and gof if
(i)
f
x
=
e
x
,
g
x
=
log
e
x
(ii)
f
x
=
x
2
,
g
x
=
cos
x
(iii)
f
x
=
|
x
|
,
g
(
x
)
=
sin
x
(iv)
f
x
=
x
+
1
,
g
x
=
e
x
(v)
f
x
=
sin
-
1
x
,
g
x
=
x
2
(vi)
f
x
=
x
+
1
,
g
x
=
sin
x
(vii)
f
x
=
x
+
1
,
g
x
=
2
x
+
3
(viii)
f
x
=
c
,
c
∈
R
,
g
x
=
sin
x
2
(ix)
f
x
=
x
2
+
2
,
g
x
=
1
-
1
1
-
x
Q.
Let
f
(
x
)
=
|
x
−
2
|
+
|
x
−
3
|
+
|
x
−
4
|
and
g
(
x
)
=
f
(
x
+
1
)
. Then
Q.
Let
f
(
x
)
=
[
x
[
x
]
]
,
g
(
x
)
=
[
x
[
1
x
]
]
and
h
(
x
)
=
[
[
x
]
x
]
,
, then
lim
x
→
2
−
f
(
x
)
+
lim
x
→
1
2
+
g
(
x
)
+
lim
x
→
2
+
h
(
x
)
=
Q.
Let
f
(
x
)
=
3
x
−
2
−
1
x
+
3
and
g
(
x
)
=
x
2
−
4
x
+
19
x
2
+
x
−
6
. If
f
(
x
)
=
g
(
x
)
, then
x
=
Q.
Let
f
(
x
)
and
g
(
x
)
are two function of
x
such that
f
(
x
)
+
g
(
x
)
=
e
x
and
f
(
x
)
−
g
(
x
)
=
e
−
x
then
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Explore more
Even Extension of a Function
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app