Verified answer

for x = inf

we have lim f = lim (sqrt(x) + sqrt(x-1) / (sqrt(x) - 1) = lim (only the highest powers of x are needed)

= lim (sqrt(x) + sqrt(x) / (sqrt(x)) = 2

for x = 1

note that (sqrt(x) + sqrt(x-1) for x = 1 gives 1

In the divisor, we have sqrt(1) - 1 = 0

so the limit is + infinity if we approach x = 1 from the right

and the limit is - inf if we approach x = 1 from the left