The range of the function
2018
The range of the function
Answer: D. (0,1) — Function: f(x) = x^2 / (1 + x^2) For all real x, x^2 ≥ 0 and 1 + x^2 > 0, so f(x) = x^2/(1 + x^2) ≥ 0. For any finite real x, x^2 < 1 + x^2, so f(x) = x^2/(1…
- A.
(−∞,+∞)
- B.
(0,∞)
- C.
(−∞,0)
- D.
(0,1)
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Correct answer: D
Function: f(x) = x^2 / (1 + x^2)
For all real x, x^2 ≥ 0 and 1 + x^2 > 0, so f(x) = x^2/(1 + x^2) ≥ 0.
For any finite real x, x^2 < 1 + x^2, so f(x) = x^2/(1 + x^2) < 1. The limit as x → ±∞ is 1, but 1 is never reached for any finite x.
At x = 0, f(0) = 0, so the value 0 is attained.
Conclusion: The range of f is [0,1).
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