Respuesta :
Given:
Given that the functions [tex]f(x)=9 x+5[/tex] and [tex]g(x)=-4x^2-6x+3[/tex]
We need to determine the value of the function [tex](f \circ g)(-9)[/tex]
First, we shall determine the value of the function [tex](f \circ g)(x)[/tex]
The value of the function [tex](f \circ g)(x)[/tex]:
Let us determine the value of the function [tex](f \circ g)(x)[/tex]
Thus, we have;
[tex](f \circ g)(x)=f[g(x)][/tex]
[tex]=f(-4x^2-6x+3)[/tex]
[tex]=9(-4x^2-6x+3)+5[/tex]
[tex]=-36x^2-54x+27+5[/tex]
[tex](f \circ g)(x)=-36x^2-54x+32[/tex]
Thus, the value of the function is [tex](f \circ g)(x)=-36x^2-54x+32[/tex]
The value of the function [tex](f \circ g)(-9)[/tex]:
The value of the function [tex](f \circ g)(-9)[/tex] can be determined by substituting x = -9 in the function [tex](f \circ g)(x)=-36x^2-54x+32[/tex]
Thus, we have;
[tex](f \circ g)(-9)=-36(-9)^2-54(-9)+32[/tex]
[tex]=-36(81)-54(-9)+32[/tex]
[tex]=-2916+486+32[/tex]
[tex](f \circ g)(-9)=-2398[/tex]
Thus, the value of the function [tex](f \circ g)(-9)[/tex] is -2398
Hence, Option A is the correct answer.
