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Mathematics
Mathematics
Problem
Let
α
\alpha
α
be a non-zero real number. Suppose
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
is a differentiable function such that
f
(
0
)
=
1
f(0)=1
f
(
0
)
=
1
and
lim
x
→
−
∞
f
(
x
)
=
1
\lim_{x \to -\infty} f(x)=1
lim
x
→
−
∞
f
(
x
)
=
1
. If
f
′
(
x
)
=
α
f
(
x
)
+
3
f'(x)=\alpha f(x)+3
f
′
(
x
)
=
α
f
(
x
)
+
3
, for all
x
∈
R
x \in \mathbb{R}
x
∈
R
, then
f
(
−
log
e
2
)
f(-\log_e 2)
f
(
−
lo
g
e
2
)
is equal to _____. A 1 B 5 C 9 D 7
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