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# Find the range of each of the following functions.f (x) = 2-3 x , x belongs to R , x > 0

Q5 (1)  Find the range of each of the following functions.

$f (x) = 2 - 3x, x \epsilon R, x > 0.$

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Given function is

$f (x) = 2 - 3x, x \epsilon R, x > 0.$
It is given that $x > 0$
Now,
$\Rightarrow 3x > 0$
$\Rightarrow -3x < 0$
Add 2 on both the sides
$\Rightarrow -3x+2 < 0+2$
$\Rightarrow 2-3x < 2$
$\Rightarrow f(x) < 2 \ \ \ \ \ \ \ \ \ \ \ \ \ \ (\because f(x) = 2-3x)$
Therefore,
Range of function $f(x) = 2 -3x$ is  $(-\infty,2)$

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