CMAT Exam 2023 Shift 2 Solved Paper

$\mathit{F}\left(\mathit{x}\right)=|2\mathit{x}|+4$
Option $\mathit{A}:\mathit{G}\left(\mathit{x}\right)=\mathit{x}+3$

$2\mathit{x}+4=\mathit{x}+3$

Therefore, this case is not possible.
If
$-2\mathit{x}+4=\mathit{x}+3$
$3\mathit{x}=1$
$\mathit{x}=1∕3>0$
Therefore, this case is not possible.
Option $\mathit{B}$ : $\mathrm{G}\left(\mathrm{x}\right)=2\mathrm{x}-2$

$2\mathit{x}+4=2\mathit{x}-2$
This case is not possible.
If
$-2\mathit{x}+4=2\mathit{x}-2$
$\mathit{x}=1.5>0$
This case is not possible.
Option C: $\mathit{G}\left(\mathit{x}\right)=2\mathit{x}+3$
If $\mathit{x}>0$ or $\mathit{x}=0$
$2\mathit{x}+4=2\mathit{x}+3$
This case is not possible.
If
$-2\mathit{x}+4=2\mathit{x}+3$
$\mathit{x}=0.25>0$
This case is not possible.
Option D: $\mathit{G}\left(\mathit{x}\right)=3\mathit{x}-2$
If $\mathit{x}>0$ or $\mathit{x}=0$
$2\mathit{x}+4=3\mathit{x}-2$
$\mathit{x}=6$
This case is possible.
Therefore, the answer is option D.
3. D