Çözüldü Range - Domain of The Inverse Function

https://i72.servimg.com/u/f72/19/97/10/39/range10.png
https://images.collegedunia.com/public/college_data/images/entrance/sample_paper/1694683550Math Level 2 SAT Practice Test 19.pdf (The last question with no answer or solution)

x·f(x) = 1 - x
x·[ 1 + f(x) ] = 1
x = 1 / [ 1 + f(x) ]
f^(-1) (x) = 1 / (1 + x)
1 + x = 0 ⇒ x = -1
Range of f(x) is R - {-1}.