Question

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

Answer 1

f(x) = [x]² − 5 [x] + 6
Given f(x) = 0
i.e [x]² − 5 [x] + 6 = 0
Let [x] = y
i.e y² − 5y + 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)