Answer :
Certainly! Let's solve the problem step-by-step.
Given:
[tex]\[ f(x) = -3 \llbracket x - 4.5 \rrbracket \][/tex]
We need to find [tex]\( f(-17.25) \)[/tex].
1. First, substitute [tex]\( x = -17.25 \)[/tex] into the expression inside the double brackets:
[tex]\[ x - 4.5 = -17.25 - 4.5 \][/tex]
2. Calculate the value inside the brackets:
[tex]\[ -17.25 - 4.5 = -21.75 \][/tex]
3. Now, we need to take the floor value of [tex]\(-21.75\)[/tex]. The floor function, [tex]\( \llbracket \cdot \rrbracket \)[/tex], returns the greatest integer less than or equal to the given number. So:
[tex]\[ \llbracket -21.75 \rrbracket = -22 \][/tex]
4. Finally, we substitute this value back into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(-17.25) = -3 \times (-22) \][/tex]
[tex]\[ f(-17.25) = 66 \][/tex]
So, the answer is:
[tex]\[ \boxed{66} \][/tex]
Therefore, the correct choice is [tex]\( A \)[/tex] 66.
Given:
[tex]\[ f(x) = -3 \llbracket x - 4.5 \rrbracket \][/tex]
We need to find [tex]\( f(-17.25) \)[/tex].
1. First, substitute [tex]\( x = -17.25 \)[/tex] into the expression inside the double brackets:
[tex]\[ x - 4.5 = -17.25 - 4.5 \][/tex]
2. Calculate the value inside the brackets:
[tex]\[ -17.25 - 4.5 = -21.75 \][/tex]
3. Now, we need to take the floor value of [tex]\(-21.75\)[/tex]. The floor function, [tex]\( \llbracket \cdot \rrbracket \)[/tex], returns the greatest integer less than or equal to the given number. So:
[tex]\[ \llbracket -21.75 \rrbracket = -22 \][/tex]
4. Finally, we substitute this value back into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(-17.25) = -3 \times (-22) \][/tex]
[tex]\[ f(-17.25) = 66 \][/tex]
So, the answer is:
[tex]\[ \boxed{66} \][/tex]
Therefore, the correct choice is [tex]\( A \)[/tex] 66.
