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let f be a bijective function such that for all x
Question:
Let f :
R
→
R
\R → \R
R
→
R
be a bijective function such that for all x ∈ R, f(x) =
∑
n
=
1
∞
a
n
x
n
\sum\limits^{\infin}_{n=1}a_nx^n
n
=
1
∑
∞
a
n
x
n
and
f
−
1
(
x
)
=
∑
n
=
1
∞
b
n
x
n
f^{-1}(x)=\sum\limits_{n=1}^{\infin}b_nx^n
f
−
1
(
x
)
=
n
=
1
∑
∞
b
n
x
n
, where f
-1
is the inverse function of f. If a
1
= 2 and a
2
= 4, then b
1
is equal to _________.
IIT JAM MA - 2023
IIT JAM MA
Updated On:
Jan 27, 2025
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Correct Answer:
0.49 - 0.51
Solution and Explanation
The correct answer is 0.49 to 0.51. (approx)
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y
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x
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(
x
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2
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y
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z
2
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{
(
x
,
y
,
z
)
∈
R
3
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x
2
+
y
2
+
z
2
≤
a
2
and
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2
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y
2
≥
b
2
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.
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f
(
x
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=
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(
x
)
+
d
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(
x
)
d
x
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(
f
(
x
))
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(
x
)
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d
x
df
(
x
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n
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(
3
n
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2
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(
3
n
+
4
)
1
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n
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n
3
+
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(
3
n
)
3
n
+
n
3
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n
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n
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o
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(
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a
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3
−
1
2
1
6
0
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1
2
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1
6
1
0
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4
- aa
T
is invertible.
Q: The matrix I
4
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T
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