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
• B. one-one
• C. into
• D. onto

Answer 1

Answer: (A), (C)

The correct options are
A many-one
C into

$f\left(x\right)=\frac{x^2}{1+x^2}$

It is clearly evident that, $f\left(x\right)=f(-x)$

Therefore, f(x) is many-one.

Also, Since $x^2\ge 0andalso1+x^2>0$ for $x\in R$,

Therefore, $f\left(x\right)\ge 0$ for $x\in R$.

So, It does not take negative values.

Thus, It is into function.

Thus, the correct answers are A nd C.