Question

Sonia works at a bakery. The function f(x) represents the amount of money Sonia earns per loaf, where x is the number of loaves she makes. The function g(x) represents the number of bread loaves Sonia bakes , where x is the number of hours she works. Show all work to find f(g(x)), and explain what f(g(x)) represents.

Answer 1

`\begin{gathered} f(g(x)=18x^3+1 \\ f(g(x))\text{ represents the total amount of money she earns} \\ x\text{ represents the number of hours she works} \end{gathered}`

Step-by-step explanation

Step 1

let

`\begin{gathered} f(x)=9x^2+1 \\ \end{gathered}`

represents the amount of money Sonia earns per loaf,

so

`\begin{gathered} x\rightarrow independent\text{ variable}\rightarrow\\u nmbe\text{r of loafs} \\ y\rightarrow\text{ dependent variable}\rightarrow\text{ money} \\ so \\ y=f(x) \\ \text{money depends on the number of loafs} \\ y=f(x)=9x^2+1 \end{gathered}`

so, x represent the number of loaves she makes, and f(x) the money she earns

Step 2

Let

`\begin{gathered} g(x)=\sqrt[]{2x^3} \\ \end{gathered}`

g(x) represents the number of bread loaves Sonia bakes , where x is the number of hours she works.

`\begin{gathered} x\rightarrow independent\text{ variable}\rightarrow\\u nmbe\text{r of hours} \\ y\rightarrow\text{ dependent variable}\rightarrow\text{ number of loaves} \\ so \\ y=g(x) \\ \text{number of loaves depend on the number of hours she works} \\ y=g(x)=\sqrt[]{2x^3}^{} \end{gathered}`

so

if we do

`f(g(x))`

we are evaluating the function of a function

so

`\begin{gathered} f(x)=9x^2+1 \\ \text{money}=9(numberofloaves)^2+1 \end{gathered}`

but, the number of floaves dependes on g , so

`\begin{gathered} f(g(x)=9(g(x))^2+1 \\ f(g(x)=9(\sqrt[]{2x^3})^2+1 \\ f(g(x)=9(2x^3)^{}+1 \\ f(g(x)=18x^3+1 \\ \end{gathered}`

`\begin{gathered} f(x)=9x^2+1 \\ \text{money}=9(numberofloaves)^2+1 \\ \text{money}=9(g(x))^2+1 \\ \text{money}=9(\sqrt[]{2x^3})^2+1=f(g(x)=9(2x^3)+1=18x^3 \\ \text{therefore the function} \\ f(g(x))\text{ represents the money she earn} \\ \text{and x is the number of hours she works } \end{gathered}`

so,in short

`\begin{gathered} f(g(x)=18x^3+1 \\ f(g(x))\text{ represents the total amount of money she earns} \\ x\text{ represents the number of hours she works} \end{gathered}`

I hope this helps you