Question

What is the domain and range for `f(x)=sqrt(2x-8)`?

Answer 1

The domain is: `[4,oo)`
The range is: `(0,oo)`

Explanation:

`f(x)=sqrt(2x-8)=>` square root of negative number is not real:
hence the domain is calculated as follow:
`2x-8>=0`
`2x>=8`
`x>=4`
In interval form:
`[4 , oo)`
Now to find the range, consider the possible minimum and the maximum values of y for the valid domain, so in this case the range is all positive real numbers:
`y>0`
`(0,oo)`