Question

Which of the following is the inverse of the equation above?
y = (x - 10^2)

Answer 1

Your expression is ambiguous. Two interpretations and their inverses:

1) If y = x - 10^2 = x - 100, then solve for x:
x = y + 100.
Swapping variables gives the inverse function f⁻¹(x) = x + 100.

2) If you meant y = (x - 10)^2, then swapping gives x = (y - 10)^2, so
y = 10 ± √x.
This is not a single-valued function unless you restrict the domain. For example,
- if the original domain is x ≥ 10, f⁻¹(x) = 10 + √x;
- if the original domain is x ≤ 10, f⁻¹(x) = 10 − √x.

If you have the multiple-choice options, paste them and I’ll pick the correct one.