If [tex]$f(x)=-2[x]+8$[/tex], what is [tex]$f(-1.8)$[/tex]?
A. 4
B. 6
C. 10
D. 12
Answer (2)
Find the greatest integer less than or equal to -1.8: [ − 1.8 ] = − 2 .
Substitute this value into the function: f ( − 1.8 ) = − 2 ( − 2 ) + 8 .
Simplify the expression: f ( − 1.8 ) = 4 + 8 = 12 .
The final answer is 12 .
Explanation
Understanding the Problem We are given the function f ( x ) = − 2 [ x ] + 8 , where [ x ] represents the greatest integer less than or equal to x . We need to find the value of f ( − 1.8 ) .
Finding the Greatest Integer First, we need to find the greatest integer less than or equal to − 1.8 . This is denoted by [ − 1.8 ] . The greatest integer less than or equal to − 1.8 is − 2 .
Calculating f(-1.8) Now, we substitute the value of [ − 1.8 ] into the function f ( x ) = − 2 [ x ] + 8 . So, we have f ( − 1.8 ) = − 2 [ − 1.8 ] + 8 f ( − 1.8 ) = − 2 ( − 2 ) + 8 f ( − 1.8 ) = 4 + 8 f ( − 1.8 ) = 12
Final Answer Therefore, f ( − 1.8 ) = 12 .
Examples
The floor function is used in many real-life applications, such as calculating taxes or determining the number of items that can fit into a container. For example, if a tax rate is 2.5% on income, and the tax is calculated on the greatest integer of the income, then the floor function is used. Similarly, if you want to pack boxes of size 1.8 cubic feet into a container of 12 cubic feet, you can fit floor(12/1.8) = floor(6.666...) = 6 boxes into the container.
The value of f ( − 1.8 ) is 12 when evaluating the function f ( x ) = − 2 [ x ] + 8 . This is determined by first finding the greatest integer less than or equal to − 1.8 , which is − 2 , and then substituting this into the function. Therefore, the correct answer is D .12 .
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