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Mathematics
Problem
For real-valued functions
f
f
f
and
g
g
g
, the quotient function
(
f
g
)
(
x
)
\left(\dfrac{f}{g}\right)(x)
(
g
f
)
(
x
)
is defined at
x
=
a
x=a
x
=
a
provided
a
a
a
lies in the domains of both
f
f
f
and
g
g
g
and which one of the following additional conditions holds? a)
g
(
a
)
=
0
g(a)=0
g
(
a
)
=
0
b)
g
(
a
)
≠
0
g(a)\ne 0
g
(
a
)
=
0
c)
f
(
a
)
≠
0
and
g
(
a
)
≠
0
f(a)\ne 0 \;\text{and}\; g(a)\ne 0
f
(
a
)
=
0
and
g
(
a
)
=
0
d)
g
(
a
)
>
0
g(a)>0
g
(
a
)
>
0
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