Answer
$\frac{97}{4}$
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 $(f∘h)(\frac{1}{2})$. We know that $(f∘h)(x)=f(h(x))$.
Therefore, $(f∘h)(\frac{1}{2})=f(h(\frac{1}{2}))=f(\frac{1}{2}-5)=f(\frac{1}{2}-\frac{10}{2})= f(\frac{1-10}{2})=f(-\frac{9}{2})=(-\frac{9}{2})^{2}+4=\frac{-9\times-9}{2\times2}+4=\frac{81}{4}+\frac{16}{4}=\frac{81+16}{4}=\frac{97}{4}$.