How do you find the domain and range of $x + \sqrt{x - 1}$ $x + sqrt( x-1 )$ ?

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Answer 1 · 2017-05-27T16:58:53

See below.

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

$x \geq 1$ $x\geq1$ .

When $x = 1$ $x=1$ , the range (or $y$ $y$ ) is $(1) + \sqrt{1 - 1} = 1$ $(1)+sqrt(1-1)=1$ . Thus, the range of $y$ $y$ is $y \geq 1$ $ygeq1$

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

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