Mathematics: Find (f ∘ g)(-6) when f(x) = 9x + 2 and g(x) = -9x2 - 2x + 1. A.573 B.-2797 C.-24,231 D.605

Find (f ∘ g)(-6) when f(x) = 9x + 2 and g(x) =

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22.01.2022

Given that the two functions are f(x)=9x+2 and g(x)=-9x^2-2x+1

We need to determine the value of $(f \circ g)(-6)$

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

The value of $(f \circ g)(x)$ can be determined using the formula,

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

Substituting g(x)=-9x^2-2x+1 in the above formula, we get;

$(f \circ g)(x)=f[-9x^2-2x+1]$

Now, substituting $x=-9 x^{2}-2 x+1$ in the function f(x)=9x+2 , we get;

$(f \circ g)(x)=9(-9x^2-2x+1)+2$

$(f \circ g)(x)=-81x^2-18x+9+2$

$(f \circ g)(x)=-81x^2-18x+11$

Thus, the value of $(f \circ g)(x)$ is $(f \circ g)(x)=-81x^2-18x+11$

The value of $(f \circ g)(-6)$ :

The value of $(f \circ g)(-6)$ can be determined by substituting x = -6 in the function $(f \circ g)(x)=-81x^2-18x+11$

Thus, we have;

$(f \circ g)(-6)=-81(-6)^2-18(-6)+11$

$(f \circ g)(-6)=-81(36)-18(-6)+11$

$(f \circ g)(-6)=-2916+108+11$

$(f \circ g)(-6)=-2797$

Thus, the value of $(f \circ g)(-6)$ is -2797

Hence, Option B is the correct answer.

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