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Given the definitions of f(x) and g(x) below, find the value of (fºg)(-8).
f(x) = x² – 3x – 12
g(x) = -x - 12
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xero099

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.

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