If $$f(x)=|x|–\lfloor x \rfloor$$ where $$\lfloor x \rfloor$$ is the greatest integer not exceeding x, then the value of $$f(–3.5)$$ is​

Correct option is A

Solution:

$$\begin{aligned}&\textbf{Step 1: Compute } |x| \textbf{ for } x = -3.5 \\&|x| = |-3.5| = 3.5 \\\\&\textbf{Step 2: Compute } \lfloor x \rfloor \textbf{ for } x = -3.5 \\&\lfloor -3.5 \rfloor = -4 \quad \text{(since } -4 \leq -3.5 < -3\text{)} \\\\&\textbf{Step 3: Substitute into } f(x) \\&f(-3.5) = |x| - \lfloor x \rfloor = 3.5 - (-4) = 3.5 + 4 = 7.5 \\\\&\textbf{Step 4: Match with the Given Options} \\&\text{The result } f(-3.5) = 7.5 \text{ corresponds to \boxed{A}}\end{aligned}$$​