Question

If $f(x) = [8x] - 3$, where $[x]$ is the greatest integer function of $x$, then $f(\pi) =$ (where $\pi = 3.14$)

• A. 21
• B. 25
• C. 23
• D. 22

Hint:

The greatest integer function $[x]$ simply drops the fractional decimal part for any positive real value. Since $8 \times 3.14$ is slightly above 25 but safely below 26, its floor value must be exactly 25. Subtracting 3 immediately gives 22!

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
Evaluate f(x) = [8x] – 3 at x = π using π ≈ 3.14, where [·] denotes the greatest integer function.

Step 2: Key Formula or Approach:
Substitute the value, compute the product, apply the floor function, then complete the arithmetic.

Step 3: Detailed Explanation:
8 × 3.14 = 25.12. The greatest integer [25.12] = 25. Then f(π) = 25 – 3 = 22.

Step 4: Final Answer:
The value is 22, matching option (D).