Question

Show that the Modulus Function $f:R\to R$, given by $f\left(x\right)=|x|$, is neither one-one nor onto, where $|x|$ is x, if x is positive or $0$ and $|x|$ is $-x$, if x is negative.

Answer 1

Show that $f\left(x\right)=\left|x\right|$ one-one nor onto.

$\because$ For $two$ value of $x$ we get only unique value of $y.$

Hence function is neither one-one.

$\because$ $x\in R$ but $y\in (0,\infty ).$

Hence $f\left(x\right)=\left|x\right|$ is neither one-one nor onto.