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Mathematics
Mathematics
Problem
Let
a
a
a
and
b
b
b
represent real numbers and define
f
(
x
)
f(x)
f
(
x
)
as follows:
f
(
x
)
=
{
a
x
2
+
x
−
b
,
x
≤
2
a
x
+
b
,
2
<
x
<
5
2
a
x
−
7
,
x
≥
5
f(x) = \begin{cases} ax^2 + x - b, & x \le 2 \\ ax + b, & 2 < x < 5 \\ 2ax - 7, & x \ge 5 \end{cases}
f
(
x
)
=
⎩
⎨
⎧
a
x
2
+
x
−
b
,
a
x
+
b
,
2
a
x
−
7
,
x
≤
2
2
<
x
<
5
x
≥
5
a. Find the values of
a
a
a
and
b
b
b
such that
f
f
f
is a continuous function a. Find the values of
a
a
a
and
b
b
b
such that
f
f
f
is a continuous function
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