How do you find the domain and range of x + sqrt( x-1 )x+x1?

1 Answer
May 27, 2017

See below.

Explanation:

Since a square root cannot have a negative under the radical (or else it would be imaginary),

x\geq1x1.

When x=1x=1, the range (or yy) is (1)+sqrt(1-1)=1(1)+11=1. Thus, the range of yy is ygeq1y1

Thus, in interval notation, the domain of the function is [1,oo)[1,), and the range is [1,oo)[1,)