[tex]\boxed{(-1/3,0)}[/tex]
Explanation:
Remember that the absolute value function is defined as:
[tex]y=\mid f(x) \mid \\ \\ y=\left \{ {{f(x) \ \ \ x\geq 0} \atop {-f(x) \ \ \ x< 0 }} \right.[/tex]
For our function:
[tex]F(x)=\left \{ {{3x+1 \ \ \ x\geq 0} \atop {-(3x+1) \ \ \ x<0}} \right.[/tex]
So the vertex occurs when these two lines intersect:
[tex]3x+1=-(3x+1) \\ \\ 3x+1=-3x-1 \\ \\ 3x+3x=-1-1 \\ \\ 6x=-2 \\ \\ x=-1/3 \\ \\ \\ Substituting \ into \ first \ line: \\ \\ y=3(-1/3)+1 \therefore y=-1+1 \therefore y=0[/tex]
Finally the vuertex is:
[tex]\boxed{(-1/3,0)}[/tex]
Learn more:
Absolute value of complex number: https://brainly.com/question/12541796
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