Find the domain of function \( f(x) = \dfrac{\sqrt{x - 1}}{\sqrt{4 - x^2}} \).
Answers
Answered by
2
Step-by-step explanation:
The function is
f
(
x
)
=
1
√
4
−
x
2
What'under the
√
sign must be
≥
0
and we cannot divide by
0
Therefore,
4
−
x
2
>
0
⇒
,
(
2
−
x
)
(
2
+
x
)
>
0
⇒
,
{
2
−
x
>
0
2
+
x
>
0
⇒
,
{
x
<
2
x
>
−
2
Therefore,
The domain is
x
∈
(
−
2
,
2
)
Also,
lim
x
→
2
−
f
(
x
)
=
lim
x
→
2
−
1
√
4
−
x
2
=
1
O
+
=
+
∞
lim
x
→
−
2
+
f
(
x
)
=
lim
x
→
−
2
+
1
√
4
−
x
2
=
1
O
+
=
+
∞
When
x
=
0
f
(
0
)
=
1
√
4
−
0
=
1
2
The range is
[
1
2
,
+
∞
)
Answered by
0
Step-by-step explanation:
dfrac{\sqrt{x - 1}}{\sqrt{4 - x^2}} \). is the answer
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