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Answer:
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Step-by-step explanation:
Explanation:
To find the domain, we will factor the quadratic expression in the square root to get
F
(
x
)
=
√
(
x
−
2
)
(
x
−
3
)
.
Assuming
F
:
R
→
R
, we know that
(
x
−
2
)
(
x
−
3
)
≥
0
. Consider
x
<
2
: we have
(
negative
)
(
negative
)
=
positive
≥
0
.
Consider
2
<
x
<
3
: we have
(
positive
)
(
negative
)
=
negative
<
0
.
Consider
x
>
3
: we have
(
positive
)
(
positive
)
=
positive
≥
0
.
Therefore, the domain of
F
is
x
∈
(
−
∞
,
2
]
∪
[
3
,
∞
)
.
For the range of
F
, we know that the square root function returns non-negative numbers so we know that the range of
F
is
y
∈
[
0
,
∞
)
.
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