Evaluate the function $h ( x ) = \left[ \left[ \frac { 1 } { 2 } x + 9 \right] \right]$ for x = 6.
A) h(x) = 9
B) h(x) = 3
C) h(x) = -12
D) h(x) = 12
E) h(x) = -3

Question

Evaluate the function $h ( x ) = \left[ \left[ \frac { 1 } { 2 } x + 9 \right] \right]$ for x = 6.  
A) h(x) = 9
B) h(x) = 3
C) h(x) = -12
D) h(x) = 12
E) h(x) = -3

Quizplus · Accepted Answer

The greatest integer function, denoted by $\left[ x \right]$, gives the greatest integer less than or equal to x. So, $\left[ \frac { 1 } { 2 } x + 9 \right]$ gives the greatest integer less than or equal to $\frac { 1 } { 2 } x + 9$. For x = 6, $\frac { 1 } { 2 } x + 9 = \frac { 1 } { 2 } ( 6 ) + 9 = 3 + 9 = 12$. The greatest integer less than or equal to 12 is 12. Therefore, h(6) = 12.

Evaluate the Function h(x)=[[12x+9]]h ( x ) = \left[ \left[ \frac { 1 } { 2 } x + 9 \right] \right]h(x)=[[21​x+9]]

Evaluate the Function $h ( x ) = \left[ \left[ \frac { 1 } { 2 } x + 9 \right] \right]$