Question

Samantha works at a bakery. The function f(x) = 3x2 − 5 represents the amount of money Samantha earns per cookie, where x is the number of cookies she makes. The function g of x equals square root of quantity 5 times x cubed end quantity represents the number of cookies Samantha bakes per hour, where x is the number of hours she works. Find f(g(x)), and explain what it represents.

Answer 1

f(g(x)) = 15x³ - 5

Explanation:

how confusingly described.

let me try and summarize what I understood :

f(x) = 3x² - 5

money earned when baking x cookies.

g(x) = sqrt(5x³)

the amount of cookies baked in x hours.

f(g(x)) now calculates how much money she earns when baking for x hours.

it is basically very simple : instead of f(x) we have f(g(x)), so g(x) is used as argument/variable in f instead of just plain x.

therefore,

f(g(x)) = 3×(sqrt(5x³))² - 5

with x now representing the baking hours, but f(...) calculating the overall money earned, by implicitly (!) calculating the amount of cookies baked in that time and taking that result automatically to calculate the earned money.

let's simplify this a little bit more.

f(g(x)) = 3×(sqrt(5x³))² - 5 = 3×(5x³) - 5 = 15x³ - 5