Question

The function for the cost of materials to make a biscuit is f(x) = four-fifths x + 4, where x is the number of biscuits. The function for the selling price of those biscuits is g(f(x)), where g(x) = 4x + 5. Find the selling price of 15 biscuits.

Answer 1

\(\bf {\color{brown}{ f(x)}}=\cfrac{4}{5}x+4\qquad g(x) = 4x + 5
\\ \quad \\
g(\quad {\color{brown}{ f(x)}}\quad )=4({\color{brown}{ f(x)}}) + 5\implies g(\quad {\color{brown}{ f(x)}}\quad )=4\left({\color{brown}{ \cfrac{4}{5}x+4}}\right) + 5
\\ \quad \\
\textit{so for 15 biscuits}
\\ \quad \\
g(\quad {\color{brown}{ f({\color{blue}{ 15}})}}\quad )=4\left({\color{brown}{ \cfrac{4}{5}{\color{blue}{ 15}}+4}}\right) + 5\)

Answer 2

I really don't understand this what so ever

Answer 3

well. notice the "red" function, f(x)

it gets "swallowed into" the other function, g(x)

Answer 4

that's what g( f(x) ) means
means that for any "x" in g(x) replace each of them by whatever f(x) is

in this case f(x) is several terms