Question

Let $f:R\to R$ be a mapping, such that $f\left(x\right)=\frac{x^2}{1+x^2}$ Then, f is

• A. Many – one into
• B. One – one
• C. Into
• D. Onto

Answer 1

The correct option is A Many – one into

$f:R\to R$, where $f\left(x\right)is\frac{x^2}{1+x^2}$
$\Rightarrow$ f is many - one.
As, $f(-x)=f\left(x\right)$ and range of $f\left(x\right)ϵ[0,1)⊏$ codomain.
$\therefore$ f is into.
Hence many – one into