Q. If $R$ denotes the set of all real numbers, then the function $f:R \rightarrow R$ defined by $f(x) = |x|$ is
A) One-one only
B) Onto only
C) Both one-one and onto
D) Neither one-one nor onto
Explanation
(d)
The given function is
$f(x) = |x| = \left\{ \begin{array}{r}
x,\ x \geq 0 \\
x,\ x < 0
\end{array} \right.\$
And $f:R \rightarrow R$, then it is clear that function is neither one-one nor onto.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.