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Byju's Answer
Standard XII
Mathematics
Differentiation of a Determinant
If f x=4 x+36...
Question
If
f
x
=
4
x
+
3
6
x
-
4
,
x
≠
2
3
, show that fof(x) = x for all
x
≠
2
3
. What is the inverse of f?
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Solution
f
o
f
x
=
f
f
x
=
f
4
x
+
3
6
x
-
4
=
4
4
x
+
3
6
x
-
4
+
3
6
4
x
+
3
6
x
-
4
-
4
=
16
x
+
12
+
18
x
-
12
24
x
+
18
-
24
x
+
16
=
34
x
34
=
x
⇒
f
o
f
x
=
x
=
I
X
,
where
I
is an identity function.
So,
f
=
f
-
1
Hence,
f
-
1
=
4
x
+
3
6
x
-
4
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