Question

If $R$ denotes the set of all real number, then the function $f:R\to R$ defined $f\left(x\right)=\left|x\right|$ is:

• A. One-one only
• B. Onto only
• C. Both one-one and onto
• D. Neither one-one and onto

Answer 1

The correct option is D Neither one-one and onto

$\text{f}\left(x\right)=|x|\ge 0$ for all $x$

So the range of f is $[0,\infty )\ne$ co domain $\Rightarrow$ $f$ is not onto

Also $\text{f}(-1)=\text{f}\left(1\right)=1\Rightarrow$ $f$ is many one (not one-one)