Question

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

Answer 1

value of $x$	value of $\left[x\right]$	$f\left(x\right)=-|x|$	whether real number
2	|2 |=2	-2	yes
1	|1|=0	-1	yes
0	|0|=0	0	yes
-1	|-1|=1	-1	yes
-2	|-2|=2	-2	yes

Here we are given a real function

Hence, both domain and range should be real numbers

From the above table

$X$ can be any real number

and $f\left(X\right)$ will always be negative or zero

All these are real values.

Here, value of domain $(Xx$ can be negative number

Hence, Domain =$R$ (all real number)

we note that the range $f\left(x\right)$ is $0$ or negative numbers

So, range cannot be positive

Hence, Range =Non positive real number.