y = 5 / (x + 5) is a valid formula for any value of x except x = -5. This is not valid, as it makes the denominator zero. The domain is therefore:

(-infinity, 0) U (0, infinity).

Find x in terms of y:

y(x + 5) = 5

x + 5 = 5 / y

x = (5/y) – 5

This is valid for any value of y except y = 0.

The range is:

(-infinity,0) U (0, infinity).

2.

y = 2sqrt(x^2 – 1) is valid provided x^2 – 1 >= 0.

Negative numbers do not have square roots.

x^2 – 1 >= 0 means x >= 1 or x <= -1. The domain is thererfore: (-infinity, -1] U [1, infinity). By letting x approach infinity or - infinity, you can make y as large as you like. Because the square root is always +ve or 0, y cannot be less than 0. The range is therefore: [0, infinity).