Question

If $f(x) = 3[x] + 5\{x + 1\}$, where $[x]$ is greatest integer function of $x$ and $\{x\}$ is fractional part function of $x$, then $f(-1.32) =$

• A. -4.6
• B. -2.6
• C. -7.4
• D. -3.4

Hint:

Recall the property $\{x + n\} = \{x\}$ for any integer $n$. Thus $\{x + 1\} = \{x\}$, which can simplify calculations.

Answer 1

The Correct Option is B

Step 1: Find the greatest integer part.
For $x = -1.32$, the greatest integer not above it is $[-1.32] = -2$.

Step 2: Handle the fractional part.
Note $\{x+1\} = \{x\}$ because adding a whole number does not change the fractional part. With $x+1 = -0.32$ and $[-0.32] = -1$, we get $\{x+1\} = -0.32 - (-1) = 0.68$.

Step 3: Put the pieces in.
\[ f(-1.32) = 3(-2) + 5(0.68) = -6 + 3.4. \]

Step 4: Add.
$-6 + 3.4 = -2.6$. \[ \boxed{-2.6} \]