Question

The range of the function $f\left(x\right)=2x-[2x-5]$ is
(where $[.]$ denotes the greatest integer function)

• A. $(5,7)$
• B. $[5,7)$
• C. $(5,6)$
• D. $[5,6)$

Answer 1

The correct option is D $[5,6)$

$f\left(x\right)=2x-[2x-5]\Rightarrow f\left(x\right)=2x-\left[2x\right]+5\Rightarrow f\left(x\right)=\left\{2x\right\}+5\Rightarrow f\left(x\right)\in [5,6)[\because \left\{y\right\}\in [0,1)]$