Question

How do you find the domain of `f @ g` given `f(x)= sqrt(x-1)` and `g(x)= 1/(x-7)`?

Answer 1

`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`