Final answer:
The inverse of the function y = x^2 - 12 is y = sqrt(x + 12) since you need to reverse the square operation by taking the square root of both sides, considering only the positive root.
Step-by-step explanation:
To find the inverse of the function y = x^2 - 12, we need to reverse the operations that have been applied to x. First, we add 12 to both sides of the equation to obtain y + 12 = x^2. Since we are looking for x in terms of y, we take the square root of both sides to find x, which gives us x = ±√(y + 12). Because we are dealing with a function, we only take the positive root, as the negative root would violate the function definition by giving us a second value of x for one value of y. Therefore, the inverse function is y = √(x + 12).
Step 1: Swap x and y: x = y^2 - 12
Step 2: Solve for y: y^2 = x + 12
Step 3: Take the square root of both sides: y = ±√(x + 12)