Question

Which of the following functions is the correct inverse for the function f(x)=√x-2, {x|x³, x|)?

A. f⁻¹(x)=√x+2
B. f⁻¹(x)=√x-2

Answer 1

The correct inverse function for f(x) = √x - 2 is f⁻¹(x) = (x + 2)², as squaring is the inverse operation to taking the square root.

Step-by-step explanation:

To find the inverse function of f(x) = √x - 2, where x ≥ 3, we need to reverse the operations that have been performed on x. In the original function, the square root is applied, and then 2 is subtracted. To reverse this, we need to first add 2 to x and then square the result (as squaring is the inverse operation to taking the square root).

Therefore, the correct inverse function would be f⁻¹(x) = (x + 2)². Options A and B provided are incorrect because they do not include squaring, which is necessary to undo the square root. Also, note that the inclusion of x ≥ 3 ensures the function is monotonic and has an inverse.