Answer:
domain: x ≥ 2
Explanation:
Given a function with domain x ≥ -5 and range y ≥ 2, you want the domain of its inverse.
Domain
The domain of an inverse function is the same as the range of the function.
The domain is x ≥ 2.
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Additional comment
If a function tells you ...
y = f(x)
The inverse function is ...
x = f(y) ⇒ y = f⁻¹(x)
The domain and range of the inverse function are swapped from those of the original function.