Question

Find the requested function value.

Answer 1

Given:

Given that the functions $f(x)=9 x+5$ and $g(x)=-4x^2-6x+3$

We need to determine the value of the function $(f \circ g)(-9)$

First, we shall determine the value of the function $(f \circ g)(x)$

The value of the function $(f \circ g)(x)$:

Let us determine the value of the function $(f \circ g)(x)$

Thus, we have;

$(f \circ g)(x)=f[g(x)]$

               $=f(-4x^2-6x+3)$

               $=9(-4x^2-6x+3)+5$

               $=-36x^2-54x+27+5$

$(f \circ g)(x)=-36x^2-54x+32$

Thus, the value of the function is $(f \circ g)(x)=-36x^2-54x+32$

The value of the function $(f \circ g)(-9)$:

The value of the function $(f \circ g)(-9)$ can be determined by substituting x = -9 in the function $(f \circ g)(x)=-36x^2-54x+32$

Thus, we have;

$(f \circ g)(-9)=-36(-9)^2-54(-9)+32$

                 $=-36(81)-54(-9)+32$

                 $=-2916+486+32$

$(f \circ g)(-9)=-2398$

Thus, the value of the function $(f \circ g)(-9)$ is -2398

Hence, Option A is the correct answer.