Question

g(x) = x - 6
domain of g:
done
k(x) = \sqrt{x}
domain of k: x \geq 0
range of k: y \geq 0

Explanation:

Step1: Identify the function type

The function \( g(x) = x - 6 \) is a linear function (a polynomial function of degree 1).

Step2: Determine the domain of a linear function

For linear functions of the form \( f(x)=mx + b \) (where \( m \) and \( b \) are real numbers), there are no restrictions on the values of \( x \) that can be input. In other words, \( x \) can be any real number. This is because we can substitute any real number for \( x \) and perform the arithmetic operation (multiplication and addition/subtraction) to get a valid output \( y \).

Answer:

All real numbers (or \( (-\infty, \infty) \) or \( x \in \mathbb{R} \))