x^6/(x^12+1) find range
Answers
Answered by
0
Step-by-step explanation:
Domain is all values except
x
=
−
4
and
x
=
3
range is from
1
2
to
1
.
Explanation:
In a rational algebraic function
y
=
f
(
x
)
, domain means all values that
x
can take. It is observed that in the given function
f
(
y
)
=
x
2
−
x
−
6
x
2
+
x
−
12
,
x
cannot take values where
x
2
+
x
−
12
=
0
Factorizing this becomes
(
x
+
4
)
(
x
−
3
)
=
0
. Hence domain is all values except
x
=
−
4
and
x
=
3
.
Range is values that
y
can take. Although, one may have to draw a graph for this, but here as
x
2
−
x
−
6
=
(
x
−
3
)
(
x
+
2
)
and hence
f
(
y
)
=
x
2
−
x
−
6
x
2
+
x
−
12
=
(
x
−
3
)
(
x
+
2
)
(
x
+
4
)
(
x
−
3
)
=
x
+
2
x
+
4
=
1
−
2
x
+
4
and hence range is from
1
2
to
1
.
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