Question

$f:[-1,1]\to [-1,1]$ is defined by $f\left(x\right)=x\left|x\right|$. This function is

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

Answer 1

Answer: (D)

bijective

$f\left(x\right)=x\mid x\mid$
$=\{\begin{array}{cc}{x}^2,& x>0\\ -x^2,& x<0\end{array}$
$f\left(x\right)$ is one - one & onto in its domain.
$\therefore$ $f\left(x\right)$ is bijective.