Answer
$\frac{23}{6}$
Work Step by Step
We are given that $f(x)=x^{2}+4$, $g(x)=2x+3$, and $h(x)=x-5$.
We are asked to find $(g∘f)(-\frac{1}{2})$. We know that $(g∘f)(x)=g(f(x))$.
Therefore, $(g∘f)(-\frac{1}{2})=g(f(-\frac{1}{2}))=g((-\frac{1}{2})^{2}+4)=g(\frac{-1\times-1}{2\times2}+4)=g(\frac{1}{4}+\frac{16}{4})=g(\frac{1+16}{4})=g(\frac{17}{4})=2(\frac{17}{4})+3=\frac{2\times17}{4}+\frac{12}{4}=\frac{34}{4}+\frac{12}{4}=\frac{34+12}{4}=\frac{46}{12}=\frac{46\div2}{12\div2}=\frac{23}{6}$.