Range of function f(x)=sqrt-x^2-6x-5
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Step-by-step explanation:
y
=
√
x
2
−
6
x
+
5
What is under the square root sign is
≥
0
Therefore,
x
2
−
6
x
+
5
≥
0
We factorise the inequality
(
x
−
1
)
(
x
−
5
)
≥
0
Let
f
(
x
)
=
(
x
−
1
)
(
x
−
5
)
We build a sign chart
a
a
a
a
x
a
a
a
a
−
∞
a
a
a
a
a
a
1
a
a
a
a
a
a
a
a
a
5
a
a
a
a
a
a
a
+
∞
a
a
a
a
x
−
1
a
a
a
a
−
a
a
a
a
0
a
a
a
+
a
a
a
0
a
a
a
a
+
a
a
a
a
x
−
5
a
a
a
a
−
a
a
a
a
0
a
a
a
−
a
a
a
0
a
a
a
a
+
a
a
a
a
f
(
x
)
a
a
a
a
a
+
a
a
a
a
0
a
a
a
−
a
a
a
0
a
a
a
a
+
Therefore,
f
(
x
)
≥
0
, when
x
∈
(
−
∞
,
1
]
∪
[
5
,
+
∞
)
graph{sqrt(x^2-6x+5) [-10, 10, -5, 5]}
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