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:
The given function $f(x) = [8x] - 3$ involves the greatest integer function (or floor function), which outputs the largest integer less than or equal to the nested value. We are asked to evaluate $f(\pi)$ using the specific given decimal approximation $\pi = 3.14$.

Step 2: Key Formula or Approach:
Substitute the given value of $\pi$ into the functional expression, evaluate the inner linear product, apply the floor operation definition $[k]$, and compute the final scalar value.

Step 3: Detailed Explanation:
Substitute $x = 3.14$ into the expression for $f(x)$: $$f(\pi) = [8 \times 3.14] - 3$$ First, calculate the product inside the greatest integer brackets: $$8 \times 3.14 = 25.12$$ Now, evaluate the greatest integer value of $25.12$: $$[25.12] = 25$$ Substitute this integer value back into the complete equation block: $$f(\pi) = 25 - 3 = 22$$

Step 4: Final Answer:
The evaluated value of $f(\pi)$ is 22, which corresponds to option (D).