Question

The function for the cost of materials to make a hat is f(x)=1/2x+1 where x is the number of hats. The function for the selling price of those hats is g(f(x)) where g(x)=x+2. Find the selling price of 10 hats. A. 6 B.8 C. 10 or D. 12

Answer 1

`\bf \begin{cases} f(x)=\cfrac{1}{2}x+1\\\\ g(x)=x+2\\ g(~~f(x)~~)=\textit{selling price} \end{cases}\\\\ -------------------------------\\\\ \boxed{x=10}\qquad f(10)=\cfrac{1}{2}10+1\implies f(10)=5+1\implies \boxed{f(10)=6}\\\\ -------------------------------\\\\ g(~~f(x)~~)=[f(x)]+2\implies g(~~f(10)~~)=[f(10)]+2 \\\\\\ g(~~f(10)~~)=\boxed{6}+2\implies g(~~f(10)~~)=8`