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Mathematics
Mathematics
Problem
Let
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
f(x+y) = f(x) + f(y)
f
(
x
+
y
)
=
f
(
x
)
+
f
(
y
)
for all
x
x
x
and
y
y
y
. If the function
f
(
x
)
f(x)
f
(
x
)
is continuous at
x
=
0
x = 0
x
=
0
, show that
f
(
x
)
f(x)
f
(
x
)
is continuous for all
x
x
x
.
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