The function y = square root sign x is translated using the rule (x, y) → (x – 7, y + 2)to create f(x). What is the domain of f(x)? {x | x > –7} {x | x > 7} {x | x > –2} {x | x > 2} square root x

Answer:Second option {x | x > 7}Step-by-step explanation:We have the function [tex]y = \sqrt{x}[/tex]We know that the square root of a negative number has no solution in the real ones. Therefore the domain of this function is [tex]x > 0[/tex]When applying the transformation: [tex](x, y) \to (x - 7, y + 2)[/tex] we have a translation of the original function in 7 units to the right and 2 units to the top: [tex]f(x) = \sqrt{x-7} + 2[/tex]In the same way we must guarantee that [tex](x-7)> 0[/tex]Then [tex]x > 7[/tex]. Therefore the domain of f(x) is {x | x > 7}