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Mathematics
Mathematics
Problem
If the function
f
(
x
)
=
{
3
a
x
+
b
,
for
x
>
1
11
,
for
x
=
1
5
a
x
−
2
b
,
for
x
<
1
f(x) = \begin{cases} 3ax + b, & \text{for } x > 1 \\ 11, & \text{for } x = 1 \\ 5ax - 2b, & \text{for } x < 1 \end{cases}
f
(
x
)
=
⎩
⎨
⎧
3
a
x
+
b
,
11
,
5
a
x
−
2
b
,
for
x
>
1
for
x
=
1
for
x
<
1
is continuous at
x
=
1
x = 1
x
=
1
, find the values of
a
a
a
and
b
b
b
.
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