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Mathematics
Problem
Let
f
(
x
)
=
x
2
−
k
x
+
k
x
−
k
f(x)=\dfrac{x^{2}-kx+k}{x-k}
f
(
x
)
=
x
−
k
x
2
−
k
x
+
k
, where
k
k
k
is a non-zero real constant. For which value(s) of
k
k
k
is
f
(
x
)
f(x)
f
(
x
)
defined for all real
x
x
x
and hence behaves as a polynomial function? a)
k
=
1
k=1
k
=
1
b)
k
=
−
1
k=-1
k
=
−
1
c) No such non-zero real value of
k
k
k
exists d) All non-zero real numbers
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