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Mathematics
Mathematics
Problem
For the function
g
k
(
x
)
=
x
2
−
k
g_k(x)=x^{2}-k
g
k
(
x
)
=
x
2
−
k
where
k
∈
R
k\in\mathbb R
k
∈
R
, let
f
(
x
)
=
ln
x
f(x)=\ln x
f
(
x
)
=
ln
x
. Determine all real values of
k
k
k
for which the domain of
(
f
∘
g
k
)
(
x
)
(f\circ g_k)(x)
(
f
∘
g
k
)
(
x
)
is
R
\mathbb R
R
.
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