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Byju's Answer
Standard XII
Mathematics
Strictly Increasing Functions
Simplify the ...
Question
Simplify the following expressions and evaluate them as directed:
(i)
x
2
(
3
−
2
x
+
x
2
)
for x=1;x=-1;
x
=
2
3
a
n
d
x
=
−
1
2
.
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Solution
f
(
x
)
=
x
2
(
3
−
2
x
+
x
2
)
x
=
1
f
(
x
)
=
1
2
[
3
−
2
(
1
)
+
(
1
)
2
]
⇒
1
[
3
−
2
+
1
]
⇒
2
x
=
−
1
f
(
x
)
=
(
−
1
)
2
[
3
−
2
(
−
1
)
+
(
−
1
)
2
]
⇒
1
[
3
+
2
+
1
]
⇒
6
x
=
2
3
f
(
x
)
=
(
2
3
)
2
[
3
−
2
(
2
3
)
+
(
2
3
)
2
]
⇒
4
9
[
3
−
4
3
+
4
9
]
⇒
4
9
[
27
−
12
+
4
9
]
⇒
4
9
×
19
9
⇒
76
81
x
=
−
1
/
2
f
(
x
)
=
(
−
1
2
)
2
[
3
−
2
(
−
1
2
)
+
(
−
1
2
)
2
]
⇒
1
4
[
3
+
1
+
1
4
]
⇒
1
4
[
12
+
4
+
1
4
]
⇒
17
16
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