Find the domain of the function, f(x) =(x2+5x-6)/(x2-5x+6)
Answers
Answered by
1
Answer:
For the domain, the denominator must be
≠
0
Therefore,
The domain is
R
−
{
2
,
3
}
For the range, let rewrite the function
y
=
x
2
+
5
x
−
6
x
2
−
5
x
+
6
y
(
x
2
−
5
x
+
6
)
=
x
2
+
5
x
−
6
y
x
2
−
x
2
−
5
y
x
−
5
x
+
6
y
+
6
=
0
(
y
−
1
)
x
2
−
5
(
y
+
1
)
x
+
6
(
y
+
1
)
=
0
....................
(
1
)
Let 's calculate the discriminant of equation
(
1
)
Δ
≥
0
25
(
y
+
1
)
2
−
24
(
y
−
1
)
(
y
+
1
)
≥
0
25
(
y
2
+
2
y
+
1
)
−
24
(
y
2
−
1
)
≥
0
y
2
+
50
y
+
49
≥
0
(
y
+
49
)
(
y
+
1
)
≥
0
The range is
(
−
∞
,
−
49
]
∪
[
−
1
,
+
∞
)
graph{(x^2+5x-6)/(x^2-5x+6) [-132.6, 134.3, -94.2, 39.3]}
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