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Mathematics
Problem
Consider the function
s
(
x
)
=
{
a
x
+
1
,
x
<
1
,
b
x
2
,
1
≤
x
<
3
,
10
−
x
,
x
≥
3
,
s(x)= \begin{cases} ax+1, & x<1,\\ bx^{2}, & 1\le x<3,\\ 10-x, & x\ge 3, \end{cases}
s
(
x
)
=
⎩
⎨
⎧
a
x
+
1
,
b
x
2
,
10
−
x
,
x
<
1
,
1
≤
x
<
3
,
x
≥
3
,
where
a
a
a
and
b
b
b
are constants. For which ordered pair
(
a
,
b
)
(a,b)
(
a
,
b
)
is
s
s
s
free of jump discontinuities on the interval
(
−
∞
,
∞
)
(-\infty,\infty)
(
−
∞
,
∞
)
? a)
(
4
3
,
7
3
)
\left(\dfrac{4}{3},\dfrac{7}{3}\right)
(
3
4
,
3
7
)
b)
(
−
2
9
,
7
9
)
\left(-\dfrac{2}{9},\dfrac{7}{9}\right)
(
−
9
2
,
9
7
)
c)
(
7
9
,
7
9
)
\left(\dfrac{7}{9},\dfrac{7}{9}\right)
(
9
7
,
9
7
)
d)
(
−
4
9
,
5
9
)
\left(-\dfrac{4}{9},\dfrac{5}{9}\right)
(
−
9
4
,
9
5
)
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