$f: R \rightarrow R$, then $f(x)=x|x|$ will be

• A

  many-one-onto
• Correct answer
  B

  one-one-onto
• C

  many-one-into
• D

  one-one-into

Solution

Given, $f: R \rightarrow R, \quad f(x)=x|x|$ Redefined the function, $$ f(x)=\left\{\begin{aligned} -x^{2}, & x < 0 \\ 0, & x=0 \\ x^{2}, & x>0 \end{aligned}\right. $$
The graph of $f(x)$ shows that it is a bijective (one-one-onto) function.

Hence, the correct answer is option: 'B'.