Answer
$-\frac{3}{4}$
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 $(h∘f)(\frac{1}{2})$. We know that $(h∘f)(x)=h(f(x))$.
Therefore, $(h∘f)(\frac{1}{2})=h(f(\frac{1}{2})=h((\frac{1}{2})^{2}+4)=h(\frac{1}{4}+4)=(\frac{1}{4}+
\frac{16}{4})=h(\frac{1+16}{4})=h(\frac{17}{4})=\frac{17}{4}-5=\frac{17}{4}-\frac{20}{4}=\frac{17-20}{4}=\frac{-3}{4}=-\frac{3}{4}$.
