Question

If the square root of 1 over 2 x - 10 added by 3, which inequality can be used to find the domain of f(x)?

Answer 1

From the description, we have the function
`f(x)= \sqrt{ (1)/(2x-10)+3 }`
Since the square root cannot be a negative number, the only thing need to do to find the domain of the function
`f(x)` is take the expression inside the square rot and set it greater or equal than zero:

`(1)/(2x-10)+3 \geq 0`

`(6x-29)/(2x-10) \geq 0`

`(6x-29)/(2(x-5)) \geq 0`

`x \leq (29)/(6)` or
`x\ \textgreater \ 5`

We can conclude that we can use the inequality
`(1)/(2x-10)+3 \geq 0` to find the domain of
`f(x)`. Also, the domain of
`f(x)` is (∞,
`(29)/(6)`]U(5,∞).