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Mathematics
Problem
For the real parameter
a
a
a
, consider the function
f
a
(
x
)
=
(
x
−
a
)
2
x
2
−
a
,
x
≠
±
a
.
f_a(x)=\frac{(x-a)^{2}}{x^{2}-a},\qquad x\ne\pm\sqrt{a}.
f
a
(
x
)
=
x
2
−
a
(
x
−
a
)
2
,
x
=
±
a
.
For which value of
a
a
a
does
f
a
f_a
f
a
have exactly one removable discontinuity and exactly one infinite (vertical asymptote) discontinuity? a)
a
=
2
a=2
a
=
2
b)
a
=
−
1
a=-1
a
=
−
1
c)
a
=
1
a=1
a
=
1
d)
a
=
0
a=0
a
=
0
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