sing the pair of functions \( f(x)=2 x \) and \( g(x)=\sqrt{3-x} \), what is \( (f-g)(-1) \) -4 \( -2-\sqrt{2} \) 0 \( (f-g)(-1) \) does not exist.

To find \( (f-g)(-1) \), we first compute \( f(-1) \) and \( g(-1) \). For \( f(x) = 2x \), substituting \( x = -1 \) gives \( f(-1) = 2 \times (-1) = -2 \). For \( g(x) = \sqrt{3 - x} \), substituting \( x = -1 \) results in \( g(-1) = \sqrt{3 - (-1)} = \sqrt{4} = 2 \). Now, we can calculate \( (f-g)(-1) = f(-1) - g(-1) = -2 - 2 = -4 \). So the answer is \( -4 \). Now, why not dive deeper into these functions? The fun way to think about functions is to visualize them on a graph! The function \( f(x) \) is a straight line that rises steeply with a slope of 2, while \( g(x) \) represents a curve starting from 2 at \( x = -1 \) and dropping as \( x \) increases. When you're looking for the difference, think of it as determining where one graph sits above or below another! If you're curious about real-world applications, consider that linear functions like \( f(x) \) can model relationships with constant rates (like speed or cost), while functions like \( g(x) \) can be used for scenarios involving limits and boundaries (like water levels or population decay). This is all about how we can use math to describe the world around us!