Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses.
x+a
f(x)=
b
g(x)=cx−d

Task 1:

Part 1: Using the two functions listed below, insert numbers in place for the letters A, B, C, D so that f(x) and g(x) are inverses.

f(x)= x + a

           b

g(x)= cx - d

Part 2: Show your work to prove that the inverse of f(x) is g(x).

Part 3: Show work to evaluate g(f(x))

Part 4: Graph you're two functions on a coordinate plane, include a table of values for each function. Include 5 values for each function.graph the line y=x on the same graph.

Task 2:

Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model.

a√x + b + c = d

Use a constant in place of each variable a, b, c, and d. You can use positive and negative constants in your equation.

Part 2: Show your work in solving the equation. Include the work to check your solution and show that your solution is extraneous.

Part 3: Explain why the equation has an extraneous solution and the second one does not.

Task 3: Create a scenario for an arithmetic sequence. For example, Jasmine practices the piano for minutes on Monday. Every day she her practice time by . If she continues this pattern, how many minutes will practice on the 7th day? Be sure to fill in the blank's with the words that will create an arithmetic sequence. Use your scenario to write the functionfor the 7th term in your sequence using sequence notation.

Part 2: Create a scenario for geometric sequence. For example, Anthony go to the gym for

minutes on Monday. Every day he his gym time by . If you continue this pattern, how many minutes will he spend at the gym on the 5th day. Be sure to fill in the blank's with the words that will create an geometric sequence.

Use your scenario to write the functionfor the 5th term in your sequence using sequence notation.

Part 3: Use your scenario from part 2 to write a question. That will lead to using the geometric series formula. Use the formula to solve for Sn in your scenario.