Answer:
The value of [tex]f\,\circ\,g(-8)[/tex] is 16.
Step-by-step explanation:
The composition consist: in replacing the independent variable ([tex]x[/tex]) of [tex]f(x)[/tex] by [tex]g(x)[/tex]:
[tex]f(x) = x^{2}-3\cdot x -12[/tex] (1)
[tex]g(x) = -x-12[/tex] (2)
[tex]f\,\circ\,g (x) = (-x-12)^{2} - 3\cdot (-x-12) -12[/tex] (3)
[tex]f\,\circ\,g(x) = (x^{2}+24\cdot x + 144) +(3\cdot x +36) - 12[/tex]
[tex]f\,\circ\,g(x) = x^{2} +27\cdot x +168[/tex]
[tex]f\,\circ g(-8) = (-8)^{2}+27\cdot (-8) +168[/tex]
[tex]f\,\circ\,g(-8) = 16[/tex]
The value of [tex]f\,\circ\,g(-8)[/tex] is 16.
