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Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
{
∣
x
−
3
∣
x
−
3
,
x
≠
3
k
,
x
=
3
f(x)=\begin{cases}\dfrac{|x-3|}{x-3},& x\neq3\\k,& x=3\end{cases}
f
(
x
)
=
⎩
⎨
⎧
x
−
3
∣
x
−
3∣
,
k
,
x
=
3
x
=
3
For which value of
k
k
k
is
f
f
f
continuous at
x
=
3
x=3
x
=
3
? a)
k
=
1
k=1
k
=
1
b)
k
=
0
k=0
k
=
0
c) No real value of
k
k
k
makes
f
f
f
continuous at
x
=
3
x=3
x
=
3
d)
k
=
−
1
k=-1
k
=
−
1
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