Question

How do you find the domain of `f(x) = sqrt{(x - 1)/x + 4)`?

Answer 1

The condition for f(x) to be defined and real is the quantity under the square root must be non-negative: `(x - 1)/x + 4 >= 0`.

`(x - 1)/x + (4x)/x = (5x - 1)/x >= 0`
2 conditions:
`x` not zero; and `(5x - 1)/x > 0`.
So `x < 0` or `x>= 1/5`
Domain of `f`: `(-oo,0) uu [1/5 , oo)`