Question

Find the demain and range of F (x) = √9-x^2.​

Answer 1

Step-by-step explanation:

If f is a real-valued, function, then (9 - x²) must be greater than or equal to 0 for f to be defined. For every value of y, y^2+4>0. Therefore, set R of all real numbers is the Range of function y=f(x)=√x^2–4

Answer 2

Domain:
[
−
3
,
3
]

Range:
[
0
,
3
]

Explanation:
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