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Mathematics
Mathematics
Problem
Let
k
k
k
and
m
m
m
be real numbers, and define
f
(
x
)
=
{
x
2
−
k
2
x
−
k
,
x
≠
k
,
m
,
x
=
k
.
f(x)= \begin{cases} \dfrac{x^{2}-k^{2}}{x-k}, & x\neq k,\\ m, & x=k. \end{cases}
f
(
x
)
=
⎩
⎨
⎧
x
−
k
x
2
−
k
2
,
m
,
x
=
k
,
x
=
k
.
For which relationship between
m
m
m
and
k
k
k
is
f
f
f
continuous at
x
=
k
x=k
x
=
k
? a)
m
=
k
2
m=k^{2}
m
=
k
2
b)
m
=
2
k
m=2k
m
=
2
k
c) There is no real number
m
m
m
that makes
f
f
f
continuous at
x
=
k
x=k
x
=
k
d)
m
=
k
m=k
m
=
k
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