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Problem
Problem
If the function
f
:
[
1
,
∞
)
→
[
1
,
∞
)
f: [1, \infty) \rightarrow [1, \infty)
f
:
[
1
,
∞
)
→
[
1
,
∞
)
is defined by
f
(
x
)
=
2
x
(
x
−
1
)
f(x) = 2^{x(x-1)}
f
(
x
)
=
2
x
(
x
−
1
)
, then
f
−
1
(
x
)
f^{-1}(x)
f
−
1
(
x
)
is (a)
(
1
2
)
x
(
x
−
1
)
\left(\frac{1}{2}\right)^{x(x-1)}
(
2
1
)
x
(
x
−
1
)
(b)
1
2
(
1
+
1
+
4
log
2
x
)
\frac{1}{2}(1 + \sqrt{1 + 4 \log_2 x})
2
1
(
1
+
1
+
4
lo
g
2
x
)
(c)
1
2
(
1
−
1
+
4
log
2
x
)
\frac{1}{2}(1 - \sqrt{1 + 4 \log_2 x})
2
1
(
1
−
1
+
4
lo
g
2
x
)
(d) Not defined
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