Rewrite the expression using the definition of composite functions.
[tex](f\circ g)(-8)=f(g(-8))[/tex]
Start from the inner function. To solve for g(-8), substitute -8 into the value of x in g(x).
[tex](f\circ g)(-8)=f\lbrack-(-8)-12\rbrack[/tex]
Simplify the expression inside the brackets.
[tex](f\circ g)(-8)=f(8-12)=f(-4)[/tex]
To find f(-4), substitute -4 into the value of x in f(x).
[tex](f\circ g)(-8)=(-4)^2-3(-4)-12[/tex]
Simplify the expression.
[tex](f\circ g)(-8)=16+12-12=16[/tex]
Therefore, the value of the expression is 16.
