Marcello's Pizza charges a base price of 16 dollar for a...

Marcello's Pizza charges a base price of 16 dollar for a large pizza plus 1.50 dollar for each additional topping. a. Find a function $f$ that models the price of a pizza with $n$ toppings. b. Find the inverse of the function $f .$ What does $f^{-1}$ represent? c. If a pizza costs 25 dollar, how many toppings does it have?

Marcello's Pizza charges a base price of 16 dollar for a large pizza plus 1.50 dollar for each additional topping.
a. Find a function $f$ that models the price of a pizza with $n$ toppings.
b. Find the inverse of the function $f .$ What does $f^{-1}$ represent?
c. If a pizza costs 25 dollar, how many toppings does it have?

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Key Concepts

Inverse Functions

An inverse function reverses the process of the original function, effectively swapping the roles of the input and output. Finding the inverse involves solving the equation for the original function in terms of the other variable. Here, the inverse function represents determining the number of toppings based on a given pizza price.

Linear Functions

A linear function represents a relationship between two variables with a constant rate of change and can be written in the form y = mx + b, where m is the rate of change and b is the y-intercept. In this context, the cost of a pizza increases linearly with each additional topping, which is modeled by a base price plus a constant cost per topping.

Function Modeling in Real-World Applications

Function modeling involves creating a mathematical representation of a real-world situation to analyze and solve problems. In this example, the cost of a pizza is modeled as a function of the number of toppings, allowing for predictions about pricing and for determining the number of toppings given a specific price.

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