What is the domain of the function y = startroot x + 6 endroot minus 7? x greater-than-or-equal-to negative 7 x greater-than-or-equal-to negative 6 x greater-than-or-equal-to 6 x greater-than-or-equal-to 7

Domain= {}

Step-by-step explanation:

The function given is: , and we are asked to find the Domain of it. Let's recall that the Domain of a function is the set of all x-values for which the function is defined (can be evaluated rendering a real number as result). So in order to find which x-values constitute such Domain, let's investigate for which x-values we can effectively evaluate the square root of "x+6".

Notice that the square root is not defined for radicands that are negative (less than zero). The only radicands that are allowed are those greater than or equal to zero. So that is exactly the condition we want to impose on the radicand: to be greater than or equal to zero (). Our radicand is the expression: "x+6", so we write in math terms the necessary condition as:

and solve for "x" in the inequality (isolating "x" on one side:

The Domain of this function is therefore all those real "x" values that are greater than or equal to negative 6 ()