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Mathematics
Mathematics
Problem
Let the function
f
f
f
be defined by
f
(
x
)
=
{
x
2
+
3
x
−
4
x
+
1
,
x
≠
2
,
k
,
x
=
2.
f(x)=\begin{cases} \dfrac{x^{2}+3x-4}{x+1}, & x\neq 2,\\ k, & x=2. \end{cases}
f
(
x
)
=
⎩
⎨
⎧
x
+
1
x
2
+
3
x
−
4
,
k
,
x
=
2
,
x
=
2.
Find the value of
k
k
k
that makes
f
f
f
continuous at
x
=
2
x=2
x
=
2
.
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