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: Understanding the Question:
We need to evaluate the function $f(x) = 3[x] + 5\{x + 1\}$ at $x = -1.32$.

Step 2: Key Formula or Approach:
Use the definitions: $[x]$ is the greatest integer $\le x$, and $\{x\} = x - [x]$. Note that $\{x+1\} = \{x\}$.

Step 3: Detailed Explanation:
For $x = -1.32$:
$[x] = [-1.32] = -2$.
For the fractional part term, $x+1 = -1.32 + 1 = -0.32$.
$\{x+1\} = (x+1) - [x+1] = -0.32 - [-0.32]$.
Since $[-0.32] = -1$, $\{x+1\} = -0.32 - (-1) = 0.68$.
Now substitute into $f(x)$:
$f(-1.32) = 3(-2) + 5(0.68) = -6 + 3.4 = -2.6$.

Step 4: Final Answer:
The value of $f(-1.32)$ is $-2.6$, which corresponds to option (B).