Find its Domain & range under root 9-x2
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Answer:
The value under a square root cannot be negative, or else the solution is imaginary.
So, we need
9
−
x
2
≥
0
, or
9
≥
x
2
, so
x
≤
3
and
x
≥
−
3
, or
[
−
3.3
]
.
As
x
takes on these values, we see that the smallest value of the range is
0
, or when
x
=
±
3
(so
√
9
−
9
=
√
0
=
0
), and a max when
x
=
0
, where
y
=
√
9
−
0
=
√
9
=
3
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