Question

Find the inverse of the function y = x² – 12.

Answer 1

The inverse of the function y = x² – 12 is found by solving for x in terms of y, which involves swapping x and y, adding 12 to both sides, and then taking the square root of both sides, resulting in y = ±sqrt(x + 12). However, to have a proper function, the domain should be restricted, and the inverse function would be y = sqrt(x + 12).

Step-by-step explanation:

To find the inverse of the function y = x² – 12, we need to solve for x in terms of y. Here are the steps to find the inverse:

1. Replace y with x and x with y to reflect the inverse relationship: x = y² – 12.
2. Add 12 to both sides of the equation to isolate the quadratic term: x + 12 = y².
3. Take the square root of both sides, remembering to include both the positive and negative solutions: y = ±sqrt(x + 12).

Note that because x² is a parabolic function, it is not one-to-one. Therefore, its inverse is not a function unless we restrict the domain. To have a proper function as the inverse, we would typically restrict x to nonnegative values, which gives us y = sqrt(x + 12) for the inverse function.