The functions f and g are defined by the given equations. f x = 3 +

The correct answer is $-4.9$. The value of $f\left(-4\right)$ is the value of $f\left(x\right)$ when $x=-4$. Substituting $-4$ for $x$ in the equation $f\left(x\right)=3+\left.-2x-x^2\right|$ yields $f\left(-4\right)=3+\left.-2\left(-4\right)-{\left(-4\right)}^2\right|$, or $f\left(-4\right)=3+\left.-8\right|$, which is equivalent to $f\left(-4\right)=3+8$, or $f\left(-4\right)=11$. Since it's given that $f\left(-4\right)=c$, it follows that $c=11$ and the value of $g\left(c\right)$ is the value of $g\left(11\right)$. Substituting $11$ for $w$ in the equation $g\left(w\right)=\left.\frac{-w}{w-1}\right|-w+5$ yields $g\left(11\right)=\left.\frac{-11}{11-1}\right|-11+5$, or $g\left(11\right)=\left.-1.1\right|-6$, which is equivalent to $g\left(11\right)=1.1-6$, or $g\left(11\right)=-4.9$. Note that -4.9 and -49/10 are examples of ways to enter a correct answer.