Question 697173
You can't take the square root of a negative value. So the radicand must be non-negative (ie 0 or positive)


Radicand is positive


x - 1 is positive


{{{x - 1 >= 0}}}


{{{x >= 1}}}


Domain: Set of all real x values such that {{{x >= 1}}}


Domain in set-builder notation: <img src="http://latex.codecogs.com/gif.latex?\large \{x|x\in \mathbb{R},x \ge 1\}" title="\large \{x|x\in \mathbb{R},x \ge 1\}" />


Domain in interval notation: <img src="http://latex.codecogs.com/gif.latex?\large [1,\infty)" title="X" />


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The range of {{{g(x)=a*sqrt(x-h)+k}}} in general is the set of all y values such that {{{y >= k}}} where 'a' is some positive number.


Since k = 4, we know...


Range: Set of all real y values such that {{{y >= 4}}}


Range in set-builder notation: <img src="http://latex.codecogs.com/gif.latex?\large \{y|y\in \mathbb{R},y \ge 4\}" title="\large \{x|x\in \mathbb{R},x \ge 1\}" />


Range in interval notation: <img src="http://latex.codecogs.com/gif.latex?\large [4,\infty)" title="X" />