Inverse Functions Practice Problems

At a party, hexagonal tables are placed side by side along one side, as shown here. 1. Explain why the equation S= 4n + 2 represents the number of seats, S, as a function of the number of tables, n.

2. What domain and range make sense for this function?

3. Write an equation to represent the inverse of the given function. Explain what this inverse function tells us.

4. How many tables are needed if 94 people are attending the party? Explain your reasoning.

5. How many tables are needed if 95 people are attending the party? Explain your reasoning.

6. What domain makes sense for the inverse function? Is it the same set of values as the range of the original function? Explain your reasoning.

7. The equation y(x) = 65 + 5x defines a function, find it's inverse.

8. The equation f(t) = 3.5 - 0.5t defines a function, find it's inverse.

9. The equation P(n) = n/3 - 1.2 defines a function, find it's inverse.

10. The number of chirps that crickets make is closely related to the temperature of their environment. When the temperature is between 12 and 38 degrees Celsius, we can tell the temperature by counting the number of chirps! A formula that is commonly used to find the temperature in degrees Celsius is: Count the number of chirps in 25 seconds, divide by 3, then add 4 to get the temperature. Let m be the number of chirps that crickets make in 25 seconds and C be the temperature in degrees Celsius. a. What is the temperature when 84 chirps are heard in 25 seconds?

b. Write an equation C that defines as a function of m.

c. How many chirps would we expect to hear in 25 seconds when it is 14 degrees Celsius?

d. Write an equation that defines the inverse of the function you wrote. Explain what the inverse function tells us about the situation.