Question

Find (f ∘ g)(-6) when f(x) = 9x + 2 and g(x) = -9x2 - 2x + 1.

Answer 1

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.