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Given the definitions of f(x) and g(x) below, find the value of (fog)(-8).f(x) = x2 – 3x – 12g(x) = -1 – 12

Given The Definitions Of Fx And Gx Below Find The Value Of Fog8fx X2 3x 12gx 1 12 class=

Sagot :

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.

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