Solve the two sided inequality and show the solution on real line

Question

7 < 1-2x ≤ 10

Given two functions as:
f(x) = x2-x-1 and g(x) = 3/x
Find fog(x) also find the domain of f, g and fog

Answer 1

7 < 1-2x ≤ 10
6 < -2x ≤ 9
-3 > x ≥ -9/2
or in the more usual form ..

-9/2 ≤ x < -3

Answer 2

the second part of your question I had already answered for you yesterday, but here it is again ...

domain of f : any real number
domain of g : any real number except x ≠ 0

fog
= f(g(x))
= f(3/x)
= (3/x)^2 - 3/x - 1

clearly the domain of fog is any real number, except x≠0