Answer:
C) 4
Step-by-step explanation:
The given function is
[tex]f(x)=\left \{ {{2x+5,\:-6\:<\:x\le0} \atop {-2x+3,\:0\:<x\le4}} \right.[/tex]
The function is defined on two intervals.
The first interval is
[tex]-6\:<\:x\le0[/tex] and the second interval is [tex]\:0\:<x\le4[/tex].
[tex]-7[/tex] does not belong to any of these intervals.
[tex]-6[/tex] does not also belong to any of these intervals.
[tex]4[/tex] belongs to the interval [tex]\:0\:<x\le4[/tex].
Hence 4 is in the domain of f(x).
[tex]5[/tex] does not also belong to any of the intervals.
Therefore the correct answer is C.
