Question

$f:R\to R,f\left(x\right)=x|x|is$

• A. one-one but not onto
• B. onto but not one-one
• C. Both one-one and onto
• D. neither one-one nor onto

Answer 1

The correct option is C

Both one-one and onto

$Givethatf\left(x\right)\{\begin{array}{c}{x}^{2}ifx>0\\ 0ifx=0\\ -x^{2}ifx<0\end{array}$
draw the graph , and you'll see that f is one-one and onto.