Question 1: Given the function f(x) = 3x + 5, find its inverse function f⁻¹(x).

Answer: f⁻¹(x) = (x - 5) / 3

Question 2: Calculate f⁻¹(14) for the function f(x) = 2x - 4.

Answer: 9

Question 3: Construct the graph of y = 2x on the grid and then draw its inverse y = f⁻¹(x).

Answer: Student draws the reflection of y=2x over y=x

Question 4: If a function f(x) = x² is restricted to x ≥ 0, what is its inverse? Write the inverse function.

Answer: f⁻¹(x) = √x

Question 5: Identify the mistake in the following inverse calculation: Given f(x) = 4x - 7, the inverse is claimed to be f⁻¹(x) = (x + 7) / 4. Is this correct? If not, what is the correct inverse?

Answer: Incorrect; correct inverse is f⁻¹(x) = (x + 7) / 4

Question 6: Solve for x: f⁻¹(x) = 5, where f(x) = (x - 2)/3. What is the value of x?

Answer: 17

Question 7: A function f(x) is given by f(x) = x³. Write the inverse function f⁻¹(x).

Answer: f⁻¹(x) = ∛x

Question 8: Common misconception: True or False? The inverse of y = 5x + 2 is y = (x - 2)/5.

Answer: True

Question 9: Given that f(x) = (2x + 3)/(x - 1), find the inverse function f⁻¹(x).

Answer: f⁻¹(x) = (3 + x) / (2 - x)

Question 10: Error analysis: A student finds the inverse of f(x) = 2x + 6 as f⁻¹(x) = (x + 6)/2. Identify and correct the mistake.

Answer: Incorrect; correct inverse is f⁻¹(x) = (x - 6)/2

Question 11: Challenge: For the function f(x) = x³ + 1, find the inverse function and describe its domain and range.

Answer: f⁻¹(x) = ∛(x - 1); domain: all real x; range: all real x