Set, Relation and FunctionHard
Question
Domain of the definition of function
f(x) =
is (where [.] → G.I.F.)
f(x) =
is (where [.] → G.I.F.)Options
A.(-∞, -2) υ [-1, 2]
B.[0, 2]
C.[-1, 2]
D.(0, 2)
Solution
Case - 1 : 4 - x2 ≥ 0 and [x] + 2 > 0
x2 - 4 ≤ 0 [x] > - 2
x ∈ [- 2, 2]
x ∈ (-1, 2) x ∈ [-1, ∞)
Case - 2 : 4 - x2 ≤ 0 and [x] + 2 < 0
x ∈ [-∞ , - 2] υ [2a) [x] < - 2
x ∈ (-∞,- 2)
x ∈ (-∞ , - 2)
x ∈ [-∞ , - 2] υ [-1,2]
x2 - 4 ≤ 0 [x] > - 2
x ∈ [- 2, 2]
x ∈ (-1, 2) x ∈ [-1, ∞)
Case - 2 : 4 - x2 ≤ 0 and [x] + 2 < 0
x ∈ [-∞ , - 2] υ [2a) [x] < - 2
x ∈ (-∞,- 2)
x ∈ (-∞ , - 2)
x ∈ [-∞ , - 2] υ [-1,2]
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