Question 1: Find the inverse function of f(x) = 3x + 5.

Answer: f⁻¹(x) = (x - 5) / 3

Question 2: Calculate f⁻¹(11) for the function f(x) = 2x - 7.

Answer: 9

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

Answer: Line y=2x and its reflection y= x/2 across y=x

Question 4: If f(x) = (x+4)/2, what is the inverse function?

Answer: f⁻¹(x) = 2x - 4

Question 5: Solve for x: f⁻¹(x) = 7, given f(x) = 3x - 2.

Answer: x=23

Question 6: Identify and correct the mistake: The inverse of f(x) = x² is f⁻¹(x) = √x.

Answer: Incorrect because the inverse should be ±√x, and the original function is not one-to-one over all reals.

Question 7: Find f⁻¹(x) if f(x) = 5 - 2x.

Answer: f⁻¹(x) = (5 - x)/2

Question 8: A function f maps input x to output y. Its inverse f⁻¹ maps y back to x. If f( x ) = 4x + 1, what is f⁻¹( y )?

Answer: f⁻¹(y) = (y - 1)/4

Question 9: Plot the graph of y = (x + 3)/2 and its inverse on the grid.

Answer: Line y=(x+3)/2 and its reflection y=2x-6 across y=x

Question 10: Determine the inverse of f(x) = (2x - 4)/(x + 1).

Answer: f⁻¹(x) = (4 + x)/(2 - x)

Question 11: A function f is defined by f(x) = x² for x ≥ 0. Find its inverse and explain any restrictions.

Answer: Inverse is f⁻¹(x) = √x, with restriction x ≥ 0 to ensure the inverse is a function.

Question 12: Identify the error: A student states that the inverse of f(x) = 1/(x - 2) is f⁻¹(x) = 2 + 1/x.

Answer: Incorrect; the inverse should be f⁻¹(x) = 2 + 1/x only if properly derived. The actual inverse of f(x) = 1/(x - 2) is f⁻¹(x) = 2 + 1/x, provided x ≠ 0, but students need to verify the derivation.