Question

If $f\left(x\right)=3\left[x\right]+1,g\left(x\right)=4[x-1]-10$, then the values of $x$ for which $f\left(x\right)=g\left(x\right)$ is
(where [.] denotes the greatest integer function)

• A. $[15,16]$
• B. $[13,14)$
• C. $[14,15]$
• D. $[15,16)$

Answer 1

The correct option is D $[15,16)$

$f\left(x\right)=3\left[x\right]+1,g\left(x\right)=4[x-1]-10$
$f\left(x\right)=g\left(x\right)\Rightarrow 3\left[x\right]+1=4[x-1]-10\Rightarrow 3\left[x\right]+1=4\left[x\right]-14$
$(\because [x+I]=\left[x\right]+I,\forall I\in Z)$
$\Rightarrow 15=\left[x\right]\Rightarrow x\in [15,16)$