Maths · One-one, into and onto functions
The function defined by =\frac{x^{2}}{1+x^{2}} \forall x \in R \) is
The function \( \boldsymbol{f}: \boldsymbol{R} \rightarrow \boldsymbol{R} \) defined by \( f(x)=\frac{x^{2}}{1+x^{2}} \forall x \in R \) is
- A. one one but not onto
- B. onto but not one one
- C. a bijection
- D. neither one one nor onto
Step-by-step solution
The function f(x)=x^2/(1+x^2) is not one-one because it is even: f(-x)=f(x), so e.g., f(1)=f(-1). It is not onto because its range is [0,1) which is a proper subset of R (e.g., value 2 is not attained). Hence it is neither one-one nor onto.
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