How do you find the domain of #f @ g# given #f(x)= sqrt(x-1)# and #g(x)= 1/(x-7)#? Algebra Expressions, Equations, and Functions Domain and Range of a Function 1 Answer VinÃcius Ferraz Jun 14, 2018 #x in (7, 8]# Explanation: #f(1/(x-7)) = sqrt{1/(x-7) - 1}# #x ne 7 and 1/(x-7) - 1 >= 0# #frac{1 - x + 7}{x - 7} >= 0# #(x - 7)(x - 8) <= 0# #7 <= x <= 8# Answer link Related questions How do you determine if (-1, 4), (2, 8), (-1, 5) is a function? What is the domain for #f(x)=2x-4#? What is the domain and range for (3,1), (1,-4), and (2, 8)? What is the domain and range of a linear function? Is domain the independent or dependent variable? How do you find the domain and range of a function in interval notation? How do you find domain and range of a rational function? How do you find domain and range of a quadratic function? How do you determine the domain and range of a function? What is Domain and Range of a Function? See all questions in Domain and Range of a Function Impact of this question 1891 views around the world You can reuse this answer Creative Commons License