Question

g(x) = x - 6
domain of g: all real numbers
range of g: all real numbers
k(x) = \sqrt{x}
domain of k: x \geq 0
range of k: y \geq 0
domain of g + k: options: x \geq 0, x \geq -6, all real numbers

Explanation:

Step1: Recall domain of sum of functions

The domain of \( g + k \) is the intersection of the domain of \( g \) and the domain of \( k \).

Step2: Identify domain of \( g \) and \( k \)

Domain of \( g \): All real numbers (since \( g(x)=x - 6 \) is a linear function, defined for all real \( x \)).
Domain of \( k \): \( x\geq0 \) (since \( k(x)=\sqrt{x} \) is a square - root function, defined when the radicand is non - negative).

Step3: Find the intersection

The intersection of all real numbers and \( x\geq0 \) is \( x\geq0 \).

Answer:

\( x\geq0 \)