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)=9x^2+1
g(x)=square root 2x^3

Answer 1

Answer:

18x^3+1

Step-by-step explanation:

since g(x)=√2x^3 and f(x)=9x^2+1 then

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

this represents the amount of money Sonia earns baking loaves in x hours

Answer 2

The equation of f(g(x)) is $f(g(x)) = 9(\sqrt{2x^3})^2 + 1$, and it represents the amount of money Sonia makes when she bakes for x hours

The functions are given as:

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

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

Recall that:

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

Substitute g(x) for x

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

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

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

Hence, the equation of f(g(x)) is $f(g(x)) = 9(\sqrt{2x^3})^2 + 1$

Read more about composite functions at:

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