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Mathematics
Problem
Suppose
f
(
x
)
f(x)
f
(
x
)
and
g
(
x
)
g(x)
g
(
x
)
are two continuous functions defined for
0
≤
x
≤
1
0 \le x \le 1
0
≤
x
≤
1
. Given
f
(
x
)
=
∫
0
1
e
x
+
t
⋅
f
(
t
)
d
t
f(x) = \int_{0}^{1} e^{x+t} \cdot f(t)\,dt
f
(
x
)
=
∫
0
1
e
x
+
t
⋅
f
(
t
)
d
t
and
g
(
x
)
=
∫
0
1
e
x
+
t
⋅
g
(
t
)
d
t
+
x
,
g(x) = \int_{0}^{1} e^{x+t} \cdot g(t)\,dt + x,
g
(
x
)
=
∫
0
1
e
x
+
t
⋅
g
(
t
)
d
t
+
x
,
find the value of
g
(
0
)
−
f
(
0
)
g(0) - f(0)
g
(
0
)
−
f
(
0
)
. a.
2
3
−
e
2
\frac{2}{3-e^2}
3
−
e
2
2
b.
3
e
2
−
2
\frac{3}{e^2-2}
e
2
−
2
3
c.
1
e
2
−
1
\frac{1}{e^2-1}
e
2
−
1
1
d. 0
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