Given:f={(x,
1+x
2
x
2
):x∈R}
Domain=x
...
Mathematics, 13.05.2021 23:10 jdobes9578
Given:f={(x,
1+x
2
x
2
):x∈R}
Domain=x
range=
1+x
2
x
2
We find different values of
1+x
2
x
2
for different values of x
Value of x value of
1+x
2
x
2
−2
1+(−2)
2
(−2)
2
=
1+4
4
=
5
4
=0.8
−1
1+(−1)
2
(−1)
2
=
1+1
1
=
2
1
=0.5
0
1+0
(0)
2
=0
1
1+(1)
2
(1)
2
=
1+1
1
=
2
1
=0.5
2
1+(2)
2
(2)
2
=
1+4
4
=
5
4
=0.8
Thus, value will always lie between 0 and 1
∴ the value of range of y=
1+x
2
x
2
is always positive
Also, it lies between 0 and 1
Hence, Range is any positive integer between 0 and 1 with 0 included.
Thus, Range of f=[0,1)
Answers: 1
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