Set, Relation and FunctionHard
Question
The range of the function f(x) = 7-xPx-3 is
Options
A.{1, 2, 3}
B.{1, 2, 3, 4, 5}
C.{1, 2, 3, 4}
D.{1, 2, 3, 4, 5, 6}
Solution
f(x) = 7-xPx - 3
7 - x ≥ 0 ⇒ x ≤ 7
x - 3 ≥ 0 ⇒ x ≥ 3,
and 7 - x ≥ x - 3 ⇒ x ≤ 5
⇒ 3 ≤ x ≤ 5 ⇒ x = 3, 4, 5 ⇒ Range is {1, 2, 3}.
7 - x ≥ 0 ⇒ x ≤ 7
x - 3 ≥ 0 ⇒ x ≥ 3,
and 7 - x ≥ x - 3 ⇒ x ≤ 5
⇒ 3 ≤ x ≤ 5 ⇒ x = 3, 4, 5 ⇒ Range is {1, 2, 3}.
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