Verified answer

Domain: x > 1

Range: all real numbers.

since we cannot have do log of negative numbers or 0 thus

x - 1 > 0

or, x > 1

thus our domain is (1, α) or x > 1

for range:

either you take help of a graph or put x-1 = ε (such that x-->1 but not equal to 1 and ε is a very small number)

we will get f(x) --> -α

similarly f(x) --> +α for x-->α

thus the range is (-α, +α) or all real numbers