Q. Let $A = \lbrack - 1,\ 1\rbrack$ and $f:A \rightarrow A$ be defined as $f(x) = x|x|$ for all $x \in A$, then $f(x)$ is
A) Many-one into function
B) One-one into function
C) Many-one onto function
D) One-one onto function
Explanation
(d)
$f(x) = x|x| = \left\{ \begin{array}{r}
x^{2},\ \ x \geq 0 \\
- x^{2},\ \ \ \ x < 0
\end{array} \right.\$
[image:2_image13.emf]
Since, $- 1 \leq x \leq 1$, therefore $- 1 \leq f(x) \leq 1$
$\therefore$ Function is one-one onto.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.