Question

find the Range of f (x) = 2-3x, x€ R x>0​

Answer 1

$\large\underline{\sf{Solution-}}$

Given function is

$\rm :\longmapsto\:f(x) = 2 - 3x \: \: when \: x > 0$

Range is defined as set of those real values which is obtained on substituting the real values of x.

Now, Given that,

$\rm :\longmapsto\:x > 0$

$\rm \implies\: - x < 0$

$\rm \implies\: -3 x < 0$

$\rm \implies\: 2-3 x < 2$

$\rm \implies\: f(x) < 2$

$\bf\implies \:x \: \in \: ( - \infty , \: 2)$

More to know :-

$\boxed{ \tt{ \: x > y \: \: \rm \implies\: - x < - y \: }}$

$\boxed{ \tt{ \: x < y \: \: \rm \implies\: - x > - y \: }}$

$\boxed{ \tt{ \: x \geqslant y \: \: \rm \implies\: - x \leqslant - y \: }}$

$\boxed{ \tt{ \: x \leqslant y \: \: \rm \implies\: - x \geqslant - y \: }}$

$\boxed{ \tt{ \: |x| < y \: \: \rm \implies\: - y < x < y \: }}$

$\boxed{ \tt{ \: |x| \leqslant y \: \: \rm \implies\: - y \leqslant x \leqslant y \: }}$