find the range of 1 + x - x^2
Answers
Answered by
1
Answer:
Simplify your function
y
=
x
+
1
x
2
−
1
=
x
+
1
(
x
+
1
)
(
x
−
1
)
=
1
x
−
1
Ask yourself where the function is not defined, where the numerator is different from zero.
x
−
1
=
0
x
=
1
The domain is the real ax except 1, range is the whole real ax.
Answered by
3
Step-by-step explanation:
The denominator is
=
1
+
x
2
∀
x
∈
R
,
1
+
x
2
>
0
Therefore,
The domain of
f
(
x
)
is
x
∈
R
To determine the range, proceed as follows
y
=
1
1
+
x
2
y
(
1
+
x
2
)
=
1
y
+
y
x
2
=
1
y
x
2
=
1
−
y
x
2
=
1
−
y
y
x
=
√
1
−
y
y
The range of
f
(
x
)
is the domain of
x
(
1
−
y
y
)
>
0
y
∈
R
*
+
1
−
y
≥
0
y
≤
1
Therefore,
The range is
y
∈
(
0
,
1
]
graph{1/(1+x^2) [-11.25, 11.25, -5.625, 5.625]}
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