Let's solve the problem step-by-step to find the value of [tex]\( g(-2.3) \)[/tex], given the function [tex]\( g(x) = 2\lfloor x \rfloor - 1 \)[/tex].
1. Identify the Floor Function:
The floor function [tex]\( \lfloor x \rfloor \)[/tex] returns the greatest integer less than or equal to [tex]\( x \)[/tex].
2. Apply the Floor Function:
We need to determine [tex]\( \lfloor -2.3 \rfloor \)[/tex].
- Since [tex]\( -2.3 \)[/tex] is between [tex]\( -3 \)[/tex] and [tex]\( -2 \)[/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].
3. Substitute into the Function [tex]\( g(x) \)[/tex]:
Now we need to use this result in the function [tex]\( g(x) = 2\lfloor x \rfloor - 1 \)[/tex].
- Substitute [tex]\( \lfloor -2.3 \rfloor \)[/tex] with [tex]\( -3 \)[/tex] into the equation:
[tex]\( g(-2.3) = 2(-3) - 1 \)[/tex].
4. Calculate the Final Value:
- Perform the multiplication: [tex]\( 2 \times (-3) = -6 \)[/tex].
- Then subtract 1: [tex]\( -6 - 1 = -7 \)[/tex].
Thus, the value of [tex]\( g(-2.3) \)[/tex] is [tex]\( -7 \)[/tex]. None of the provided answer choices (7, [tex]\(-5\)[/tex], [tex]\(-4\)[/tex], [tex]\(-3\)[/tex]) match this result.
