Chapter 4 - Section 4.3 - Polynomial Functions, Graphs, and Composition - 4.3 Exercises - Page 296: 61

8

We are given that $f(x)=x^{2}+4$, $g(x)=2x+3$, and $h(x)=x-5$. We are asked to find $(f∘g)(-\frac{1}{2})$. We know that $(f∘g)(x)=f(g(x))$. Therefore, $(f∘g)(-\frac{1}{2})=f(g(-\frac{1}{2}))=f(2(-\frac{1}{2})+3)=f(-1+3)=f(2)=2^{2}+4=4+4=8$.