Find the range of the following function:
$f(x) = 2 - 3x$,where $x \in R$ and $x > 0$.
$f(x) = 2 - 3x$,where $x \in R$ and $x > 0$.
(D) Given the function $f(x) = 2 - 3x$ for $x > 0$.
Since $x > 0$,we multiply both sides by $3$:
$3x > 0$
Now,multiply by $-1$ (which reverses the inequality sign):
$-3x < 0$
Add $2$ to both sides:
$2 - 3x < 2 - 0$
$f(x) < 2$
Thus,the range of the function $f$ is the set of all real numbers less than $2$.
Therefore,the range of $f$ is $(-\infty, 2)$.
Since $x > 0$,we multiply both sides by $3$:
$3x > 0$
Now,multiply by $-1$ (which reverses the inequality sign):
$-3x < 0$
Add $2$ to both sides:
$2 - 3x < 2 - 0$
$f(x) < 2$
Thus,the range of the function $f$ is the set of all real numbers less than $2$.
Therefore,the range of $f$ is $(-\infty, 2)$.
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