If y = 2[x] + 3 & y = 3[x – 2] + 5, then find [x + y] where [.] denotes greatest integer function.

Solution :

y = 3[x – 2] + 5 = 3[x] – 1

so 3[x] – 1 = 2[x] + 3

[x] = 4 \(\implies\) 4 \(\le\) x < 5

then y = 11

so x + y will lie in the interval [15, 16)

so [x + y] = 15


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