Question

Range of f (x) = 2-3x, $xϵR,x>0is$......

Answer 1

Given:$f\left(x\right)=2-3x$ where $x\in R$,$x>0$

We find various values of $f\left(x\right)$ for $x\in R$,$x>0$

Value of $x$	value of $f\left(x\right)=2-3x$
$0.1$	$2-3\times 0.1=2-0.3=1.7$
$0.01$	$2-3\times 0.01=2-0.03=1.97$
$1$	$2-3\times 1=2-3=-1$
$2$	$2-3\times 2=2-6=-4$
$1000$	$2-3\times 1000=2-3000=-2998$

We note that value of $f\left(x\right)$ is less than $2$(not including $2$)

Hence, Range$=(-\infty ,2)$