Question

Let $f:R\to R$ defined by $f\left(x\right)=\frac{x^2}{1+x^2}$
f is

• A. injective
• B. surjective
• C. bijective
• D. neither injective nor surjective

Answer 1

Answer: (D)

neither injective nor surjective

$f\left(x\right)=\frac{x^2}{1+x^2}=1-\frac{1}{1+x^2}$
Clearly domain of $f\left(x\right)$ is $R$ and range is $[0,1)$
also $f(-1)=f\left(1\right)$. Hence this function is neither injective not surjective.