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Byju's Answer
Standard XII
Mathematics
Linear Functions
If 3 fx +5 f ...
Question
If
3
f
x
+
5
f
1
x
=
1
x
-
3
for all non-zero x, then f(x) =
(a)
1
14
3
x
+
5
x
-
6
(b)
1
14
-
3
x
+
5
x
-
6
(c)
1
14
-
3
x
+
5
x
+
6
(d) None of these
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Solution
(d) None of these
3
f
x
+
5
f
1
x
=
1
x
-
3
...(1)
Multiplying
(
1
)
by
3
:
15
f
1
x
+
9
f
(
x
)
=
3
x
-
9
.
.
.
.
.
(
2
)
Replacing
x
by
1
x
in
(
1
)
:
3
f
1
x
+
5
f
(
x
)
=
x
-
3
Multiplying
by
5
:
15
f
1
x
+
25
f
(
x
)
=
5
x
-
15
.
.
.
.
(
3
)
Solving
(
2
)
and
(
3
)
:
-
16
f
(
x
)
=
3
x
-
5
x
+
6
⇒
f
(
x
)
=
1
16
-
3
x
+
5
x
-
6
Disclaimer: The question in the book has some error, so, none of the options are matching with the solution. The solution is created according to the question given in the book.
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