Answer:
a. yes
Step-by-step explanation:
The given function is
[tex]f(x)=\left \{ {{3x-2,if\:x\le3} \atop {10-x,if\:x\:>\:3}} \right.[/tex]
[tex]f(3)=\left \{ {{3(3)-2,if\:x\le3} \atop {10-3,if\:x\:>\:3}} \right.=7[/tex]
[tex]\lim_{x \to 3^-} f(x)=3(3)-2=7[/tex]
[tex]\lim_{x \to 3^+} f(x)=10-3=7[/tex]
[tex]\Rightarrow \lim_{x \to 3} f(x)=7[/tex]
Since;
[tex]\lim_{x \to 3} f(x)=f(3)[/tex]
The function is continuous at [tex]x=3[/tex]
