Byju's Answer
Standard XII
Mathematics
Derivative of One Function w.r.t Another
20. Let f(x)=...
Question
20. Let f(x)=1/x and g(x)=1/x then
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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
)
=
|
x
−
2
|
+
|
x
−
3
|
+
|
x
−
4
|
and
g
(
x
)
=
f
(
x
+
1
)
. Then
Q.
Assertion :Let
f
(
x
)
=
(
x
+
1
)
2
−
1
∀
x
≥
−
1
and
g
(
x
)
=
−
1
+
√
x
+
1
then number of solutions of the equation
g
(
x
)
=
f
(
x
)
is two Reason:
f
(
x
)
and
g
(
x
)
are inverse of each other.
Q.
Let f(x) =
x
2
+
1
x
2
and g(x) = x -
1
x
,
x
∈
R
−
{
−
1
,
0
,
1
}
.
I
F
h
(
x
)
=
f
(
x
)
g
(
x
)
,
t
h
e
n
t
h
e
l
o
c
a
l
m
i
n
i
m
u
m
v
a
l
u
e
o
f
h
(
x
)
i
s
:
Q.
Assertion :Let the function
f
(
x
)
=
x
2
−
x
+
1
∀
x
≥
1
2
and
g
(
x
)
=
1
2
+
√
x
−
3
4
, then
f
(
x
)
=
g
(
x
)
has two solutions. Reason:
f
(
x
)
and
g
(
x
)
are inverse of each other.
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