Question

Find domain and range of the function $f\left(x\right)$ given by $f\left(x\right)=\frac{x}{1+x^2}$

• A. Domain $=R$ and Range $=N$
• B. Domain $=N$ and Range $=R$
• C. Domain $=R$ and Range $=R$
• D. Domain $=R-\left\{0\right\}$ and Range $=N$

Answer 1

The correct option is C Domain $=R$ and Range $=R$

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

For existance, $1+x^2\ne 0$ which is $\forall x\in R$

So Domain is $R$

As the above function is real over whole range gives real values

Domain=Range$=R$