Question

What is the domain and range of `f(x)= sqrt(x-4) + 2`?

Answer 1

The domain is: `x>=4`
The range is: `y>=2`

Explanation:

The domain is all the x values where a function is defined. In this case the given function is defined as long as the value under the square root sign is greater than or equal to zero, thus:
`f(x)=sqrt(x-4)+2`
The domain:
`x-4>=0`
`x>=4`
In interval form:
`[4,oo)`
The range is the all the values of a function within its valid domain, in this case the minimum value for x is 4 which makes the square root part zero, thus:
The range:
`y>=2`
In interval form:
`[2,oo)`