A function is a mapping from domain to range. The domain of the function [tex]y = \sqrt{x+6} - 7[/tex] is given as: [tex]x \geq -6[/tex] or [tex]x \in [-6, \infty)[/tex] (both are same)
One method of finding the domain of a function is to start by finding the values for which it isn't defined.
Assuming that the function [tex]y = \sqrt{x+6} - 7[/tex] is defined for only real numbers, then, as we know that:
[tex]\sqrt{x}[/tex] exists only if x is non-negative, which means for [tex]\sqrt{x+6}[/tex] to be defined, we need
[tex]x + 6 \geq 0\\x \geq -6[/tex]
No other way is there for the function to be non-existing.
Thus, the values on which the function is defined is all real numbers bigger or equal to -6. This is the domain of the given function.
Thus, the domain of the function [tex]y = \sqrt{x+6} - 7[/tex] is given as: [tex]x \geq -6[/tex] or [tex]x \in [-6, \infty)[/tex] (both are same)
Learn more about domain and range of a function here:
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