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Byju's Answer
Standard XII
Mathematics
Definition of Functions
If fx = x +...
Question
If
f
(
x
)
=
x
+
(
1
/
x
)
, show that
{
f
(
x
)
}
3
=
f
(
x
3
)
+
3
f
(
1
/
x
)
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Solution
f
(
x
)
=
x
+
1
x
⇒
f
(
x
3
)
=
x
3
+
1
x
3
...(1)
⇒
f
(
y
x
)
=
1
x
+
1
(
1
/
x
)
⇒
x
+
1
x
=
f
(
1
/
x
)
...(2)
(
f
(
x
)
)
3
=
(
x
+
1
x
)
3
=
x
3
+
(
1
x
)
3
+
3
(
x
.
1
x
)
(
x
+
1
x
)
=
(
x
3
+
1
x
3
)
+
3
(
1
)
(
x
+
1
x
)
(
f
(
x
)
)
3
=
f
(
x
3
)
+
3
f
(
1
x
)
from (1) and (2)
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