Question

Find the domain and range of the following real function :$f\left(x\right)=-|x|$

Answer 1

$f\left(x\right)=-|x|$

We know, $|x|=x,x\ge 0$

$|x|=-x,x<0$

Since, $f\left(x\right)$ is defined for $x\in R$, the domain of f is $R$.

It can be observed that the range of $f\left(x\right)=-|x|$ is all real numbers except positive real numbers.

Therefore, the range of $f$ is $(-\infty ,0]$.