Final answer:
The inverse of F(x) is F^(-1)(x) = 1/(x+1) - 5, and the domain of F(x) is all real numbers except for -5.
Step-by-step explanation:
To find the inverse of a function, we need to switch the roles of x and y and solve for y.
Starting with F(x) = 1/(x+5) -1, we can rewrite it as y = 1/(x+5) -1. To find the inverse, we switch x and y and solve for y: x = 1/(y+5) -1.
Now, solve for y: x + 1 = 1/(y+5), y+5 = 1/(x+1), y = 1/(x+1) - 5.
Therefore, the inverse of F(x) is F-1(x) = 1/(x+1) - 5.
The domain of F(x) is the set of all inputs for which the function is defined. In this case, the only restriction is that the denominator (x+5) cannot be equal to 0. So, x+5 ≠ 0, x ≠ -5.
Therefore, the domain of F(x) is all real numbers except for -5.
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