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

1 Answer
Nghi N. · 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 >= 0x−1x+4≥0.

(x - 1)/x + (4x)/x = (5x - 1)/x >= 0x−1x+4xx=5x−1x≥0
2 conditions:
xx not zero; and (5x - 1)/x > 05x−1x>0.
So x < 0x<0 or x>= 1/5x≥15
Domain of ff: (-oo,0) uu [1/5 , oo)(−∞,0)∪[15,∞)

Related questions
See all questions in Domain and Range of a Function
Impact of this question
2145 views around the world
You can reuse this answer
Creative Commons License