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Fractional Part Function

f : R → R is ...

Question

$f : R \to R$ is a function defined by $f (x) = 3 {x} - 2 | x | .$ Then the value of $f (- 0.7) - f (- 2)$ is
(Here, ${.}$ denotes the fractional part function)

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Solution

$f (x) = 3 {x} - 2 | x | \Rightarrow f (- 0.7) = 3 (0.3) - 2 (0.7) = - 0.5$
$\Rightarrow f (- 2) = 3 (0) - 2 (2) = - 4 \Rightarrow f (- 0.7) - f (- 2) = - 0.5 + 4 = 3.5$

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