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Mathematics
Mathematics
Problem
A function
f
f
f
is defined by
f
(
x
)
=
{
a
x
+
b
,
x
≤
1
,
x
2
+
a
,
1
<
x
<
4
,
6
x
−
b
,
x
≥
4.
f(x)=\begin{cases} ax+b, & x\le1,\\ x^2+a, & 1<x<4,\\ 6x-b, & x\ge4. \end{cases}
f
(
x
)
=
⎩
⎨
⎧
a
x
+
b
,
x
2
+
a
,
6
x
−
b
,
x
≤
1
,
1
<
x
<
4
,
x
≥
4.
Determine the ordered pair
(
a
,
b
)
(a,b)
(
a
,
b
)
that makes
f
f
f
continuous at both
x
=
1
x=1
x
=
1
and
x
=
4
x=4
x
=
4
. a)
(
8
,
0
)
(8,0)
(
8
,
0
)
b)
(
9
,
1
)
(9,1)
(
9
,
1
)
c)
(
7
,
1
)
(7,1)
(
7
,
1
)
d)
(
2
,
6
)
(2,6)
(
2
,
6
)
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