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Mathematics
Problem
Define
f
:
(
0
,
∞
)
→
R
f:(0,\infty)\to\mathbb R
f
:
(
0
,
∞
)
→
R
by
f
(
x
)
=
ln
x
f(x)=\ln x
f
(
x
)
=
ln
x
and
g
:
R
→
(
0
,
∞
)
g:\mathbb R\to(0,\infty)
g
:
R
→
(
0
,
∞
)
by
g
(
x
)
=
e
2
x
g(x)=e^{2x}
g
(
x
)
=
e
2
x
. Which of the following equals
(
g
∘
f
)
−
1
(
y
)
(g\circ f)^{-1}(y)
(
g
∘
f
)
−
1
(
y
)
for
y
>
0
y>0
y
>
0
? a)
1
2
ln
y
\dfrac{1}{2}\ln y
2
1
ln
y
b)
y
2
\dfrac{y}{2}
2
y
c)
y
\sqrt{y}
y
d)
y
y
y
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