Maths · One-one, into and onto functions
If \rightarrow[\mathbf{0}, \infty), \) and =\frac{\mathbf{x}}{\mathbf{1}+\mathbf
If \( \mathbf{f}:[\mathbf{0}, \infty) \rightarrow[\mathbf{0}, \infty), \) and \( \mathbf{f}(\mathbf{x})=\frac{\mathbf{x}}{\mathbf{1}+\mathbf{x}} \) then \( \boldsymbol{f} \) is
- A. one - one and onto
- B. one - one but not onto
- C. onto but not one - one
- D. neither one - one nor onto
Step-by-step solution
The function f(x)=x/(1+x) is strictly increasing (derivative positive) hence injective. For surjectivity, solving y=x/(1+x) gives x=y/(1-y). For y≥1, x is not in [0,∞) (undefined or negative), so not onto.
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