Question
If \( f(x)=-2[x]+8 \), what is \( f(-1.8) ? \) 4 6 10 12
Ask by Graham May. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f(-1.8) = 12 \)
Solution
To evaluate \( f(-1.8) \) for the function \( f(x) = -2[x] + 8 \), we need to determine the value of \([x]\). Here, \([x]\) typically represents the **floor function**, which returns the greatest integer less than or equal to \( x \).
1. **Calculate \([ -1.8 ]\):**
\[
[ -1.8 ] = -2
\]
The floor of \(-1.8\) is \(-2\) because \(-2\) is the greatest integer less than \(-1.8\).
2. **Substitute into the function \( f(x) \):**
\[
f(-1.8) = -2[-1.8] + 8 = -2(-2) + 8 = 4 + 8 = 12
\]
**Answer:** 12
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Simplify this solution Bonus Knowledge
To find \( f(-1.8) \), we first need to evaluate the greatest integer function \( [-1.8] \), which gives us the greatest integer less than or equal to -1.8. That value is -2. Now, substituting \( [-1.8] \) into the function: \[ f(-1.8) = -2[-1.8] + 8 = -2(-2) + 8 = 4 + 8 = 12 \] Thus, the answer is \( 12 \).
