If f(x) =

Question:

If f(x) = [x]2 − 5 [x] + 6, then the set of values of x satisfying f(x) = 0 is __________ .

Solution:

f(x) = [x]2 − 5 [x] + 6

Given f(x) = 0

i.e [x]− 5 [x] + 6  = 0

Let [x] = y

i.e y2 − 5+ 6 = 0

i.e y2 − 3y  – 2y + 6 = 0

y(y − 3) −2 (y − 3) = 0

i.e y = 2 or y = 3 

i.e [x] = 2 or [x] = 3

here, [x] = 2 if x∈ [2, 3) and [x] = 3 if x∈ [3, 4)

∴ value of x for which f(x) = 0 are [2, 3) ∪ [3, 4)

i.e x∈ [2, 4)

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