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Mathematics
Mathematics
Problem
Define the functions
f
(
x
)
=
{
x
+
2
,
x
≤
2
,
x
−
2
,
x
>
2
,
g
(
t
)
=
1
t
−
4
(
t
≠
4
)
.
f(x)=\begin{cases} x+2, & x\le 2,\\ \sqrt{x-2}, & x>2, \end{cases} \qquad g(t)=\dfrac{1}{t-4}\;(t\ne 4).
f
(
x
)
=
{
x
+
2
,
x
−
2
,
x
≤
2
,
x
>
2
,
g
(
t
)
=
t
−
4
1
(
t
=
4
)
.
Determine the domain of the composition
g
∘
f
g\circ f
g
∘
f
. a)
(
−
∞
,
2
)
∪
(
2
,
18
)
∪
(
18
,
∞
)
(-\infty,2)\cup(2,18)\cup(18,\infty)
(
−
∞
,
2
)
∪
(
2
,
18
)
∪
(
18
,
∞
)
b)
R
∖
{
18
}
\mathbb R\setminus\{18\}
R
∖
{
18
}
c)
R
∖
{
4
}
\mathbb R\setminus\{4\}
R
∖
{
4
}
d)
R
∖
{
2
}
\mathbb R\setminus\{2\}
R
∖
{
2
}
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