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Mathematics
Mathematics
Problem
The function
f
(
x
)
=
{
k
x
2
+
1
,
x
≤
1
,
3
x
+
c
,
1
<
x
<
3
,
10
,
x
≥
3
f(x)= \begin{cases} kx^{2}+1, & x\le 1,\\ 3x+c, & 1< x <3,\\ 10, & x\ge 3 \end{cases}
f
(
x
)
=
⎩
⎨
⎧
k
x
2
+
1
,
3
x
+
c
,
10
,
x
≤
1
,
1
<
x
<
3
,
x
≥
3
is required to be continuous at both
x
=
1
x=1
x
=
1
and
x
=
3
x=3
x
=
3
. Which of the following pairs
(
k
,
c
)
(k,c)
(
k
,
c
)
satisfies this requirement? a)
(
4
,
1
)
(4,1)
(
4
,
1
)
b)
(
3
,
1
)
(3,1)
(
3
,
1
)
c)
(
1
,
3
)
(1,3)
(
1
,
3
)
d)
(
3
,
0
)
(3,0)
(
3
,
0
)
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