Final answer:
To find the inverse of the equation y = x² - 12x, interchange the x and y variables, solve for y, and use the quadratic formula to find the inverse.
Step-by-step explanation:
To find the inverse of the equation y = x² - 12x, we need to interchange the x and y variables and solve for the new y.
Step 1: Replace y with x and x with y:
x = y² - 12y
Step 2: Rearrange the equation to solve for y:
y² - 12y - x = 0
Step 3: Use the quadratic formula to find the inverse of the equation.
y = (12 ± √(12² - 4(1)(-x))) / 2
y = 6 ± √(36 + 4x)
The error made in finding the inverse may be in the steps of rearranging the equation or using the quadratic formula. Care should be taken to ensure correct substitutions and algebraic simplifications.