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Mathematics
Mathematics
Problem
Let
f
f
f
be defined on set
A
A
A
and
g
g
g
on set
B
B
B
. For the quotient function
(
f
g
)
(
x
)
=
f
(
x
)
g
(
x
)
\bigl(\tfrac{f}{g}\bigr)(x)=\dfrac{f(x)}{g(x)}
(
g
f
)
(
x
)
=
g
(
x
)
f
(
x
)
to exist, which of the following correctly describes its domain? a)
(
A
∪
B
)
∖
{
x
∣
g
(
x
)
=
0
}
(A\cup B)\setminus\{x\mid g(x)=0\}
(
A
∪
B
)
∖
{
x
∣
g
(
x
)
=
0
}
b)
B
∖
{
x
∣
g
(
x
)
=
0
}
B\setminus\{x\mid g(x)=0\}
B
∖
{
x
∣
g
(
x
)
=
0
}
c)
(
A
∩
B
)
∖
{
x
∣
g
(
x
)
=
0
}
(A\cap B)\setminus\{x\mid g(x)=0\}
(
A
∩
B
)
∖
{
x
∣
g
(
x
)
=
0
}
d)
A
∩
B
A\cap B
A
∩
B
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