Let $f:[-2, 2]→ [-4, 4]$ be a function defined by $f(x)= x|x|$, then f i s:
Answer & explanation
Correct answer: option 4
The correct answer is Option (1) → One-one but not onto
$f(x)=x|x|=\left\{\begin{matrix}x^2,&x≥0\\-x^2,&x<0\end{matrix}\right.$
$f(x_1)=f(x_2)=x_1|x_1|=x_2|x_2|$
$⇒x_1=x_2$ (one one function)
Not onto for x = 2
Also f(x) is an Onto function as Range = Co- Domain