Respuesta :
Given that the two functions are [tex]f(x)=9x+2[/tex] and [tex]g(x)=-9x^2-2x+1[/tex]
We need to determine the value of [tex](f \circ g)(-6)[/tex]
The value of [tex](f \circ g)(x)[/tex]:
The value of [tex](f \circ g)(x)[/tex] can be determined using the formula,
[tex](f \circ g)(x)=f[g(x)][/tex]
Substituting [tex]g(x)=-9x^2-2x+1[/tex] in the above formula, we get;
[tex](f \circ g)(x)=f[-9x^2-2x+1][/tex]
Now, substituting [tex]x=-9 x^{2}-2 x+1[/tex] in the function [tex]f(x)=9x+2[/tex], we get;
[tex](f \circ g)(x)=9(-9x^2-2x+1)+2[/tex]
[tex](f \circ g)(x)=-81x^2-18x+9+2[/tex]
[tex](f \circ g)(x)=-81x^2-18x+11[/tex]
Thus, the value of [tex](f \circ g)(x)[/tex] is [tex](f \circ g)(x)=-81x^2-18x+11[/tex]
The value of [tex](f \circ g)(-6)[/tex]:
The value of [tex](f \circ g)(-6)[/tex] can be determined by substituting x = -6 in the function [tex](f \circ g)(x)=-81x^2-18x+11[/tex]
Thus, we have;
[tex](f \circ g)(-6)=-81(-6)^2-18(-6)+11[/tex]
[tex](f \circ g)(-6)=-81(36)-18(-6)+11[/tex]
[tex](f \circ g)(-6)=-2916+108+11[/tex]
[tex](f \circ g)(-6)=-2797[/tex]
Thus, the value of [tex](f \circ g)(-6)[/tex] is -2797
Hence, Option B is the correct answer.
