Question

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

• A. Injective
• B. Surjective
• C. Bijective
• D. None of these

Answer 1

The correct option is D None of these

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

Since, $1+x^2>0forx\in R$

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

Thus, f(x) is not a onto function as it does not take non-positive values.

It can be easily seen that $f\left(x\right)=f(-x).$

Therefore, f(x) is not one-one function.

So, D is correct answer.