To find the value of [tex]\( f(-1.8) \)[/tex] for the function [tex]\( f(x) = -2[x] + 8 \)[/tex], the steps to solve are as follows:
1. Identify the greatest integer function, denoted by [tex]\([x]\)[/tex]. The greatest integer function, also known as the floor function, returns the largest integer less than or equal to [tex]\( x \)[/tex].
2. Determine [tex]\([x]\)[/tex] for [tex]\( x = -1.8 \)[/tex].
- For [tex]\( x = -1.8 \)[/tex], [tex]\([x]\)[/tex] is the greatest integer less than or equal to [tex]\(-1.8\)[/tex].
- The largest integer less than or equal to [tex]\(-1.8\)[/tex] is [tex]\(-2\)[/tex].
3. Substitute [tex]\([x]\)[/tex] into the function [tex]\( f(x) \)[/tex].
- Given [tex]\( [ -1.8 ] = -2 \)[/tex], we substitute [tex]\([x] = -2\)[/tex] into the function:
[tex]\[
f(-1.8) = -2[-2] + 8
\][/tex]
4. Simplify the expression:
[tex]\[
f(-1.8) = -2 \times (-2) + 8
\][/tex]
[tex]\[
f(-1.8) = 4 + 8
\][/tex]
[tex]\[
f(-1.8) = 12
\][/tex]
Therefore, the correct value of [tex]\( f(-1.8) \)[/tex] is [tex]\( 12 \)[/tex]. The answer is [tex]\( \boxed{12} \)[/tex].
