Question

The range of the function $f\left(x\right)=[x-9]-(x-3)$ is

• A. $(-7,-6)$
• B. $[-7,-6]$
• C. $(-7,-6]$
• D. $[-7,-6)$

Answer 1

The correct option is C $(-7,-6]$

$f\left(x\right)=[x-9]-(x-3)$
$\Rightarrow f\left(x\right)=\left[x\right]-9-x+3$
$\Rightarrow f\left(x\right)=-(x-[x\left]\right)-6$
$\Rightarrow f\left(x\right)=-\left\{x\right\}-6\Rightarrow f\left(x\right)\in (-7,-6][\because \left\{y\right\}\in [0,1)]$