Find the domain and range of the following
functions given by
i) l x-4 l / (x-4)
ii) √(16-x^2)
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Answered by
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Answer:
Given Below
Step-by-step explanation:
(2) Answer
Domain :
−
4
≤
x
≤
4
, in interval notation :
[
−
4
,
4
]
Range:
0
≤
f
(
x
)
≤
4
, in interval notation :
[
0
,
4
]
Explanation:
f
(
x
)
=
√
16
−
x
2
, for domain under root should not be
negative quantity.
16
−
x
2
≥
0
or
16
≥
x
2
or
x
2
≤
16
∴
x
≤
4
or
x
≥
−
4
. Domain :
−
4
≤
x
≤
4
or
[
−
4
,
4
]
Range :
f
(
x
)
is maximum at
x
=
0
,
f
(
x
)
=
4
and
f
(
x
)
is minimum at
x
=
4
,
f
(
x
)
=
0
Range :
0
≤
f
(
x
)
≤
4
or
[
0
,
4
]
Domain :
−
4
≤
x
≤
4
, in interval notation :
[
−
4
,
4
]
Range:
0
≤
f
(
x
)
≤
4
, in interval notation :
[
0
,
4
]
graph{(16-x^2)^0.5 [-10, 10, -5, 5]}
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