Answer:
- (-∞, ∞)
- (-∞, 3) ∪ (5, ∞)
- (2, 6)
Step-by-step explanation:
a) f(x) > 0 for all x: (-∞, ∞)
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b) f(x) > 4 for x < 3 and x > 5: (-∞, 3) ∪ (5, ∞)
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c) f(x) < 5 for 2 < x < 6: (2, 6)
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<em>Comment on the notation</em>
The brackets are round brackets (parentheses) because the end points are not included in the interval. The first number corresponds to the left end of the interval on the number line. The second number corresponds to the right end of the interval on the number line. When intervals are disjoint, their union is indicated with the appropriate symbol.
If the end number is included in the interval, a square bracket is used:
1 < x ≤ 3 ⇒ (1, 3]
