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Mathematics
Mathematics
Problem
A function
g
g
g
is defined by
g
(
x
)
=
{
k
x
2
−
5
k
,
x
<
3
,
2
x
+
1
,
x
≥
3
,
g(x)=\begin{cases} kx^2-5k, & x<3,\\[4pt] 2x+1, & x\ge 3, \end{cases}
g
(
x
)
=
{
k
x
2
−
5
k
,
2
x
+
1
,
x
<
3
,
x
≥
3
,
where
k
k
k
is a real constant. (a) Determine the value of
k
k
k
that makes
g
g
g
continuous at
x
=
3
x=3
x
=
3
. (b) Using your value of
k
k
k
, verify algebraically that
g
g
g
is continuous at
x
=
3
x=3
x
=
3
.
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