To solve the problem [tex]\( g(x) = 2 \lfloor x \rfloor - 1 \)[/tex] for [tex]\( x = -2.3 \)[/tex], we need to use the floor function and then evaluate the given formula. Here are the steps:
1. Find [tex]\( \lfloor x \rfloor \)[/tex] when [tex]\( x = -2.3 \)[/tex]:
- The floor function [tex]\( \lfloor x \rfloor \)[/tex] returns the greatest integer less than or equal to [tex]\( x \)[/tex].
- For [tex]\( x = -2.3 \)[/tex], the greatest integer less than or equal to [tex]\(-2.3\)[/tex] is [tex]\(-3\)[/tex].
- Thus, [tex]\( \lfloor -2.3 \rfloor = -3 \)[/tex].
2. Substitute [tex]\( \lfloor -2.3 \rfloor \)[/tex] into the function [tex]\( g(x) = 2 \lfloor x \rfloor - 1 \)[/tex]:
- Replace [tex]\( \lfloor x \rfloor \)[/tex] with [tex]\(-3\)[/tex] in the formula.
- So, [tex]\( g(-2.3) = 2(-3) - 1 \)[/tex].
3. Calculate the expression:
- [tex]\( 2(-3) = -6 \)[/tex]
- Therefore, [tex]\( g(-2.3) = -6 - 1 = -7 \)[/tex].
So, [tex]\( g(-2.3) = -7 \)[/tex].
The correct answer is [tex]\( \boxed{-7} \)[/tex].
