Expand your knowledge base with the help of IDNLearn.com's extensive answer archive. Our platform is designed to provide reliable and thorough answers to all your questions, no matter the topic.
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.