Question

Can someone check my work, if it’s right? Any corrects made please comment below!

Answer 1

`f(g(x))` represents the amount of money Sonia earns by working for
`x` hours.

`g(x)` tells us how many loaves Sonia can bake in
`x` hours. So, for example, if she works for 10 hours, she can bake
`√(2\cdot10^3)\approx44` loaves of bread.

`f(x)` tells us how much money she earns for the number of loaves
`x` sold. So, for example, if Sonia bakes 10 loaves of bread, then she earns
`9\cdot10^2+1=901` (insert units of money).

The composite function
`f(g(x))` is really a function of time, not number of loaves. So if Sonia works for 10 hours, then she makes about 44 loaves of bread, and so would earn about
`9\cdot44^2+1=17,425`.

Answer 2

f(g(x)) = 18x³ +1 . . . . . the amount Sonia earns baking bread for x hours

Explanation:

Your work is fine as far as it goes. You need to be aware that the square of a square root is the content of the radical:

`(√(2x^3))^2=2x^3`

That is sort of the point of a square root: squaring it give the original value.

Using this fact, you can simplify your result to ...

`f(g(x))=9(√(2x^3))^2+1=9(2x^3)+1=18x^3+1`

You have correctly observed that this represents the amount Sonia earns baking bread for x hours.