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 $\sqrt{2\cdot10^3}\approx44$ 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

Answer:

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

Step-by-step 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:

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

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 ...

$f(g(x))=9(\sqrt{2x^3})^2+1=9(2x^3)+1=18x^3+1$

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