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Mathematics
Problem
Let
f
(
x
)
=
{
3
x
+
1
x
<
2
k
x
2
−
5
x
≥
2
f(x)=\begin{cases} 3x+1 & x<2 \\ kx^2-5 & x\ge 2 \end{cases}
f
(
x
)
=
{
3
x
+
1
k
x
2
−
5
x
<
2
x
≥
2
Determine the value of
k
k
k
that ensures
f
f
f
is continuous at
x
=
2
x=2
x
=
2
. a)
k
=
3
4
k=\dfrac{3}{4}
k
=
4
3
b)
k
=
3
k=3
k
=
3
c)
k
=
6
k=6
k
=
6
d)
k
=
1
2
k=\dfrac{1}{2}
k
=
2
1
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