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 per hour, where x is the number of hours she works. Show all work to find f(g(x)), and explain what f(g(x)) represents.
f(x) = 9x2 + 1
g of x equals the square root of the quantity 2 x cubed

Answer 1

Answer:

$f(g(x))=18x^3+1$

f(g(x)) represents the amount of money Sonia earns per loaf given the number of hours Sonia works.

Step-by-step explanation:

We are given two functions:

$f(x)=9x^2+1$

Which represents the amount of money Sonia earns per loaf (the range), where x is the number of loaves she makes (the domain).

And the function:

$g(x)=\sqrt{2x^3}$

Which represents the number of loaves Sonia bakes per hour (the range), where x is the number of hours she works (the domain).

We want to find f(g(x)). So, by substitution:

$f(g(x))=9(\sqrt{2x^3})^2+1$

Square:

$f(g(x))=9(2x^3)+1$

Simplify:

$f(g(x))=18x^3+1$

When we substituted g(x) for the x in f(x), the range of g(x) became the domain for f(x).

So, the domain of g(x) and the range of f(x) remained the same.

Therefore, f(g(x)) represents the amount of money Sonia earns per loaf (range of f(x)) given the number of hours Sonia works (domain of g(x)).

Answer 2

Answer:

A

Step-by-step explanation:

The dude above me has the right idea but its Dollars/hour not loaves/hour. also i took test and it was right.