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Byju's Answer
Standard XII
Mathematics
Composite Function
If fx=3x+24...
Question
If
f
(
x
)
=
3
x
+
2
4
x
−
1
and
g
(
x
)
=
x
+
2
4
x
−
3
, prove that
(
g
o
f
)
(
x
)
=
(
f
o
g
)
(
x
)
=
x
.
Open in App
Solution
f
(
x
)
=
3
x
+
2
4
x
−
3
&
g
(
x
)
=
x
+
2
4
x
−
3
g
o
f
(
x
)
=
g
(
f
(
x
)
)
=
g
3
x
+
2
4
x
−
1
+
2
4
3
x
+
2
4
x
−
1
−
3
=
3
x
+
2
+
8
x
−
2
12
x
+
8
−
12
x
+
3
=
11
x
11
=
x
.
f
(
x
)
=
x
+
2
4
x
−
3
&
g
(
x
)
=
x
+
2
4
x
−
3
g
o
f
(
x
)
=
g
(
f
(
x
)
)
=
g
3
x
+
2
4
x
−
1
+
2
4
x
+
2
4
x
−
1
−
1
=
3
x
+
6
+
8
x
−
6
4
x
+
8
−
4
x
+
3
=
11
x
11
=
x
.
∴
f
o
g
(
x
)
=
g
o
f
(
x
)
=
x
.
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0
Similar questions
Q.
Given
f
(
x
)
=
8
x
,
x
≠
0
and
fog
(
x
)
=
4
x
, find the (i)
g
(
x
)
(ii) the value of
x
, when
gof
(
x
)
=
3
.
Q.
Assertion :If
f
(
x
)
=
s
g
n
(
x
)
and
g
(
x
)
=
x
(
1
−
x
2
)
,
then
f
o
g
(
x
)
and
g
o
f
(
x
)
are continuous everywhere Reason:
f
o
g
(
x
)
=
⎧
⎨
⎩
−
1
,
x
∈
(
−
1
,
0
)
∪
(
1
,
∞
)
0
,
x
∈
{
−
1
,
0
,
1
}
1
,
x
∈
(
−
∞
,
−
1
)
∪
(
0
,
1
)
and
g
o
f
(
x
)
=
0
,
∀
x
∈
R
Q.
f
:
R
→
R
,
f
(
x
)
=
x
2
,
g
:
R
→
R
,
g
(
x
)
=
2
x
, then
x
|
(
f
o
g
)
(
x
)
=
(
g
o
f
)
)
(
x
)
=
.
.
.
.
.
.
.
.
.
Q.
Given, f(x) =
l
o
g
1
+
x
1
−
x
and g(x)
=
3
x
+
x
3
1
+
3
x
2
then (fog) (x) equals
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
=
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