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NCERT Class XI Mathematics - Relations and Functions - Solutions

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Question : 30
Total: 36
Let f = {(x,
x2
1+x2
):x∊R} be a function from R into R. Determine the range of f.
Solution:  
We have f = {(x,
x2
1+x2
):x∊R}
Clearly, domain of f is R.
Let y =
x2
1+x2
It is clear that
x2
1+x2
 ≥ 0 (Since x2 ≥ 0 and 1 + x2 ≥ 0)
and x2 < 1 + x2 ⇒
x2
1+x2
 < 1
⇒ 0 ≤ y < 1
Hence, range of f is [0, 1).
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