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Mathematics
Mathematics
Problem
For
x
≠
1
,
4
x\neq1,4
x
=
1
,
4
, define
h
(
x
)
=
(
x
2
−
1
)
(
x
−
4
)
(
x
−
1
)
(
x
−
4
)
.
h(x)=\frac{(x^{2}-1)(x-4)}{(x-1)(x-4)}.
h
(
x
)
=
(
x
−
1
)
(
x
−
4
)
(
x
2
−
1
)
(
x
−
4
)
.
To make
h
h
h
continuous at both
x
=
1
x=1
x
=
1
and
x
=
4
x=4
x
=
4
, which pair of values should be assigned to
h
(
1
)
h(1)
h
(
1
)
and
h
(
4
)
h(4)
h
(
4
)
, respectively? a)
h
(
1
)
=
1
,
h
(
4
)
=
5
h(1)=1,\;h(4)=5
h
(
1
)
=
1
,
h
(
4
)
=
5
b)
h
(
1
)
=
2
,
h
(
4
)
=
4
h(1)=2,\;h(4)=4
h
(
1
)
=
2
,
h
(
4
)
=
4
c)
h
(
1
)
=
2
,
h
(
4
)
=
5
h(1)=2,\;h(4)=5
h
(
1
)
=
2
,
h
(
4
)
=
5
d)
h
(
1
)
=
0
,
h
(
4
)
=
3
h(1)=0,\;h(4)=3
h
(
1
)
=
0
,
h
(
4
)
=
3
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