If $y = 2 [x] + 3$ and $y = 3 [x] - 1,$ find the value of $[x + y]$ , Where $[.]$ denotes GIF.

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Solution

Given: $y = 2 [x] + 3 & y = 3 [x] - 1,$
$\Rightarrow 2 [x] + 3 = 3 [x] - 1 \Rightarrow [x] = 4$
Using the property: $[x] \leq x < [x] + 1$
$\Rightarrow 4 \leq x < 5 \dots (i)$
Also, $y = 2 [x] + 3 = 11$
$\Rightarrow 4 + 11 \leq x + y < 5 + 11 \Rightarrow 15 \leq x + y < 16 \Rightarrow [x + y] = 15$

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