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phospho

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I'm asked to find the inverse and the domain of the inverse which is the range of f(x). I've found the inverse but for the domain, I put x ε ℝ however the answer is x≥2

I can see how they got the answer but why is my answer incorrect. This is how I'm seeing it:

for example: x = - 8 => f(x) = 2 - ±√(-8+9) leading to f(x) = 1, 3: but they seem to be taking the positive root only. Why?