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Mathematics
Mathematics
Problem
Suppose
f
(
x
)
=
{
a
+
b
x
,
x
<
1
4
,
x
=
1
b
−
a
x
,
x
>
1
f(x) = \begin{cases} a + bx, & x < 1 \\ 4, & x = 1 \\ b - ax, & x > 1 \end{cases}
f
(
x
)
=
⎩
⎨
⎧
a
+
b
x
,
4
,
b
−
a
x
,
x
<
1
x
=
1
x
>
1
and if
lim
x
→
1
f
(
x
)
=
f
(
1
)
\lim_{x \to 1} f(x) = f(1)
lim
x
→
1
f
(
x
)
=
f
(
1
)
, what are possible values of
a
a
a
and
b
b
b
?
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