Question

How do you find the range of `x + sqrt( x-1 )`?

Answer 1

The range is `[1,+oo)`

Explanation:

Set `f(x)=x+sqrt(x-1)` this is defined for `x-1>=0=>x>=1`.Hence
the domain is `[1,+oo)`

Hence the minimum value for f(x) is at x=1 then f(1)=1 and the range is

`[f(1),+oo)=[1,+oo)`