If f(x) = x/(1 + |x|), then f is:

If f(x) = x/(1 + |x|), then f is:

• A. one-one but not onto
• B. onto but not one-one
• C. bijective from R to (−1, 1)
• D. neither one-one nor onto

Answer: C) bijective from R to (−1, 1)

Explanation: f is strictly increasing. For x ≥ 0, f(x) = x/(1+x), range [0, 1). For x < 0, f(x) = x/(1−x), range (−1, 0). Total range is (−1, 1). f is one-one. So it's a bijection from R to (−1, 1).