Please help I’m clueless.
Find the domain of the function (enter answer in interval notation):
h(x)=1/ fourth root of xsquared – 9x
any ideas?
✅ Answers
Answerer 1
The fourth root must take arguments that are positive or zero. However, you are dividing, so you need to rule out zero…this leaves the following inequality:
x² – 9x > 0
–> factor
x(x – 9) > 0
This is true when you have a positive times a positive or negative times a negative…if it’s easier you can simply make a sign chart (it will flip at all zeros):
positive … x = 0 … negative … x = 9 … positive
That is:
x < 0 and x – 9 < 0 –> x < 9 <– but if x is less than zero then surely it’s less than 9.
x > 0 and x – 9 > 0 –> x > 9 <– the converse, if x is greater than 9 then it’s already greater than 0.
So the domain would be:
-∞ < x < 0 ∪ 9 < x < +∞
or
x: (-∞, 0) ∪ (9, +∞)