Question 1: Find the inverse function of f(x) = 3x + 4.

Answer: f⁻¹(x) = (x - 4)/3

Question 2: Calculate f⁻¹(10) for the function f(x) = 2x - 5.

Answer: f⁻¹(10) = 7.5

Question 3: Construct the graph of y = 2x and its inverse on the grid.

Answer: Student draws y=2x and y=(x)/2.

Question 4: If f(x) = (x + 1)^2, find the inverse function f⁻¹(x).

Answer: f⁻¹(x) = √x - 1 (for x ≥ 0)

Question 5: Solve for x: f⁻¹(x) = 5, where f(x) = 2x + 3.

Answer: f⁻¹(x) = 5 ⇒ 2x + 3 = 5 ⇒ x = 1

Question 6: A function f(x) is such that f⁻¹(x) = (x - 2)/3. Find the original function f(x).

Answer: f(x) = 3x + 2

Question 7: Describe the process to find the inverse of a quadratic function, such as f(x) = x^2 + 4x + 5.

Answer: Complete the square to rewrite as (x + 2)^2 + 1, then solve for x.

Question 8: Construct the inverse of y = (x - 3)/2 and verify by composition.

Answer: Inverse is y = 2x + 3; verify that f(f⁻¹(x))=x and vice versa.

Question 9: Given f(x) = 5x - 7, find the point where f and f⁻¹ intersect.

Answer: Solve x = 5x - 7 ⇒ 4x = 7 ⇒ x = 7/4; then y = x.

Question 10: Identify and correct the mistake in finding the inverse of f(x) = 2x + 5, where a student claimed f⁻¹(x) = x - 5/2.

Answer: Incorrect because f⁻¹(x) = (x - 5)/2, not x - 5/2.

Question 11: Solve the multi-step equation: If f(x) = 4x + 1, find x such that f⁻¹(x) = 3.

Answer: f⁻¹(x)= (x - 1)/4; set (x - 1)/4=3 ⇒ x - 1=12 ⇒ x=13