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Byju's Answer
Standard XII
Mathematics
Global Maxima
The maximum v...
Question
The maximum value of
f
(
x
)
=
100
−
|
45
−
x
|
for any value of
x
is
k
−
x
then
k
is ____.
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Solution
Given
f
(
x
)
=
100
−
|
45
−
x
|
Case 1-
45
−
x
>
0
∴
|
45
−
x
|
=
45
−
x
∴
f
(
x
)
=
100
−
(
45
−
x
)
∴
f
(
x
)
=
100
−
45
+
x
∴
y
=
f
(
x
)
=
55
+
x
(1)
Case 2-
45
−
x
<
0
∴
|
45
−
x
|
=
−
(
45
−
x
)
∴
|
45
−
x
|
=
x
−
45
∴
f
(
x
)
=
100
−
(
x
−
45
)
∴
f
(
x
)
=
100
−
x
+
45
∴
y
=
f
(
x
)
=
145
−
x
(2)
Equate equations (1) and (2),
55
+
x
=
145
−
x
∴
2
x
=
145
−
55
∴
2
x
=
90
∴
x
=
45
Thus, maximum function is given by,
f
(
x
)
=
55
+
x
for
x
>
45
f
(
x
)
=
145
−
x
for
x
<
45
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Q.
The maximum value of
f
(
x
)
=
100
−
|
45
−
x
|
is
Q.
Let
f
(
x
)
=
kx
x
+
1
,
x
≠
−
1
.
If
f
(
f
(
x
)
)
=
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for all
x
≠
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, then the value of
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