question archive Task 1) 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

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Task 1)

**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.

**f(x)=**

**x+ab**

**g(x)=cx−dPart 2.** Show your work to prove that the inverse of f(x) is g(x).

**Part 3.** Show your work to evaluate g(f(x)).

**Part 4.** Graph your two functions on a coordinate plane. Include a table of values for each function. Include five values for each function. Graph the line y = x on the same graph.

Task 2

**Part 1.** 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 first equation has an extraneous solution and the second does not.

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