Question

The function $y=f\left(x\right)$, $f:R\to R$, given by $f\left(x\right)=x|x|+x^3|x|$ is-

• A. One - one into
• B. One - one onto
• C. Many one into
• D. Many one onto

Answer 1

The correct option is B One - one onto

$f\left(x\right)=\left\{\begin{array}{cc}{x}^4+x^2,& x\ge 0\\ -x^4-x^2,& x<0\end{array}\right\}$

$f^{{}^{\prime }}\left(x\right)\ge 0$
So one-one function and onto.