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: Read the function.
We have $f(x)=3[x]+5\{x+1\}$, where $[x]$ is the greatest integer not above $x$ and $\{x\}$ is the fractional part. We need $f(-1.32)$.
Step 2: Find the greatest integer part.
For $x=-1.32$, the greatest integer at or below it is $-2$. So $[x]=-2$.
Step 3: Use a fractional-part shortcut.
The fractional part repeats every whole number, so $\{x+1\}=\{x\}$. Thus we just need $\{-1.32\}$.
Step 4: Compute the fractional part.
By definition $\{x\}=x-[x]=-1.32-(-2)=0.68$.
Step 5: Substitute into f.
$f(-1.32)=3(-2)+5(0.68)$.
Step 6: Finish the arithmetic.
This is $-6+3.4=-2.6$, which is option (B).
\[ \boxed{\,f(-1.32)=-2.6\,} \]