How to find the Domain of this function?

Question

Clear["Global`*"]
f[x_] = Log[10, x + a/x - 2]
FunctionDomain[{f[x], a > 0}, x] // Reduce[#, a] &

USE

In[22]:= Clear["Global`*"]
f[x_] = Log[10, x + a/x - 2]
FunctionDomain[{f[x], a > 0}, x] // Reduce[#, a] &

Out[23]= Log[-2 + a/x + x]/Log[10]

Out[24]= (0 < x <= 2 && a > 2 x - x^2) || (x > 2 && a > 0)

The answer above is incorrect

the correct answer is as follows:

(0 < a <= 1 && (0 < x < 1 - Sqrt[1 - a] || x > 1 + Sqrt[1 - a])) || (a > 1 && x > 0)

Answer 1

FunctionDomain[{Log[10, x + a/x - 2], a > 0}, x]// Reduce[#, x] &
(*(0 < a <=1 && (0 < x < 1 - Sqrt[1 - a] || x > 1 + Sqrt[1 - a])) || (a > 1&&x > 0)*)

gives the "correct asnwer".

By the way RegionPlot[...] shows no difference between the two conditions // Reduce[#, a] & and // Reduce[#, x] & !