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

1 Answer
Nghi N. ยท Jim H
Apr 26, 2015

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)

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