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Mathematics
Mathematics
Problem
Let
f
f
f
and
g
g
g
be continuous at
x
=
3
x=3
x
=
3
. Consider the function
h
(
x
)
=
f
(
x
)
+
g
(
x
)
f
(
x
)
−
g
(
x
)
.
h(x)=\frac{f(x)+g(x)}{f(x)-g(x)}.
h
(
x
)
=
f
(
x
)
−
g
(
x
)
f
(
x
)
+
g
(
x
)
.
At
x
=
3
x=3
x
=
3
,
h
h
h
will NOT be continuous if a)
f
(
3
)
+
g
(
3
)
=
0
f(3)+g(3)=0
f
(
3
)
+
g
(
3
)
=
0
b)
f
(
3
)
=
g
(
3
)
f(3)=g(3)
f
(
3
)
=
g
(
3
)
c)
f
(
3
)
=
0
f(3)=0
f
(
3
)
=
0
d)
f
(
3
)
g
(
3
)
=
0
f(3)\,g(3)=0
f
(
3
)
g
(
3
)
=
0
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