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Mathematics
Problem
Let
f
(
x
)
=
x
+
2
f(x)=\sqrt{x+2}
f
(
x
)
=
x
+
2
with domain
x
≥
−
2
x\ge -2
x
≥
−
2
, and
g
k
(
x
)
=
1
x
−
k
g_k(x)=\dfrac{1}{x-k}
g
k
(
x
)
=
x
−
k
1
where
k
∈
R
k\in\mathbb{R}
k
∈
R
. For which values of
k
k
k
is the domain of
(
g
k
∘
f
)
(
x
)
(g_k\circ f)(x)
(
g
k
∘
f
)
(
x
)
equal to
[
−
2
,
∞
)
[-2,\infty)
[
−
2
,
∞
)
? a)
k
≤
0
k\le 0
k
≤
0
b)
k
>
0
k>0
k
>
0
c)
k
<
0
k<0
k
<
0
d)
k
=
0
k=0
k
=
0
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