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Mathematics
Mathematics
Problem
Let
f
(
x
)
f(x)
f
(
x
)
be a function such that
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
and
f
(
x
)
=
(
2
x
2
+
3
x
)
⋅
g
(
x
)
f(x) = (2x^2 + 3x) \cdot g(x)
f
(
x
)
=
(
2
x
2
+
3
x
)
⋅
g
(
x
)
for all
x
x
x
where
g
(
x
)
g(x)
g
(
x
)
is continuous and
g
(
0
)
=
3
g(0) = 3
g
(
0
)
=
3
. Then,
f
′
(
x
)
f'(x)
f
′
(
x
)
is equal to a. 6 b. 9 c. 8 d. None of these
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