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Mathematics
Problem
For
a
>
0
,
a
≠
1
a>0,\,a\neq1
a
>
0
,
a
=
1
, consider the function
F
(
x
)
=
a
2
x
−
1
F(x)=a^{2x-1}
F
(
x
)
=
a
2
x
−
1
. Which option gives
F
−
1
(
x
)
F^{-1}(x)
F
−
1
(
x
)
along with its correct domain? a)
F
−
1
(
x
)
=
2
log
a
x
+
1
F^{-1}(x)=2\log_a x + 1
F
−
1
(
x
)
=
2
lo
g
a
x
+
1
, domain
(
0
,
∞
)
(0,\infty)
(
0
,
∞
)
b)
F
−
1
(
x
)
=
log
a
x
+
1
2
F^{-1}(x)=\dfrac{\log_a x +1}{2}
F
−
1
(
x
)
=
2
lo
g
a
x
+
1
, domain
(
0
,
∞
)
(0,\infty)
(
0
,
∞
)
c)
F
−
1
(
x
)
=
log
a
x
+
1
2
F^{-1}(x)=\dfrac{\log_a x +1}{2}
F
−
1
(
x
)
=
2
lo
g
a
x
+
1
, domain
R
\mathbb R
R
d)
F
−
1
(
x
)
=
log
a
x
−
1
2
F^{-1}(x)=\dfrac{\log_a x -1}{2}
F
−
1
(
x
)
=
2
lo
g
a
x
−
1
, domain
(
0
,
∞
)
(0,\infty)
(
0
,
∞
)
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