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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
{
p
x
+
1
,
x
<
1
x
2
+
q
,
x
≥
1
f(x)=\begin{cases}px+1,&x<1\\x^{2}+q,&x\ge1\end{cases}
f
(
x
)
=
{
p
x
+
1
,
x
2
+
q
,
x
<
1
x
≥
1
be continuous on
R
\mathbb R
R
and suppose that
f
(
2
)
=
7
f(2)=7
f
(
2
)
=
7
. Which one of the following pairs
(
p
,
q
)
(p,q)
(
p
,
q
)
satisfies these conditions? a)
(
5
,
5
)
(5,5)
(
5
,
5
)
b)
(
4
,
3
)
(4,3)
(
4
,
3
)
c)
(
3
,
3
)
(3,3)
(
3
,
3
)
d)
(
2
,
3
)
(2,3)
(
2
,
3
)
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