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प्रश्न
Let `f = {(x, x^2/(1+x^2)):x ∈ R}` be a function from R into R. Determine the range of f.
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उत्तर
We have `f = {(x, x^2/(1+x^2)):x ∈ R}`
Clearly, domain of f is R.
Let y = `x^2/(1 + x^2)`
It is clear that `x^2/(1 + x^2) ≥ 0`
(∵ x2 ≥ 0 and 1 + x2 ≥ 0)
and x2 < 1 + x2 => `x^2/(1 + x^2) < 1`
=> 0 ≤ y < 1
Hence, range of f is [0, 1).
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