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Nova Math - Problem Set D: Defined Functions
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Question
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No.1: For all p ≠ 2 define p* by the equation . If p =3, then p* = ...
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No.2: Let [x] be defined by the equation Then which of the following equals 2? ...
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No.3: For all a and b, define a # b to be Column A Column B 2 # 3 2 − 3 ...
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No.4: If denotes the area of a circle with diameter d, then which of the following is equal to ? ...
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No.5: For all real numbers x, y, and z, let ...
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No.6: Let [x] = x2 − 2. If [2] − [x] = x2, then x = ...
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No.7: For all real numbers a and b, where a · b ≠ 0, let . Then which of the following must be true? ...
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No.8: The operation * is defined for all non-zero x and y by the equation . Then the expression (x * y)* z...
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No.9: Let x ⊗ y =x − y − 2x. For what value of x does x ⊗ y = −y for all values of y? ...
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No.10: For all positive numbers n, What is the value of (64*)*? ...
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No.11: what is the value of − ? ...
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No.12: For all numbers N, let denote the least integer greater than or equal to N. What is the value of ? ...
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No.13: Let x⊕y = for all x and y. Column A Column B 3⊕4 9 ...
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No.14: ϕ is a function such that 1 ϕ a = 1 and a ϕ b = b ϕ a for all a and b. Which of ...
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No.15: The symbol Θ denotes one of the operations: addition, subtraction, multiplication, or division...
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No.16: 4 #12 = ...
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No.17: If x # y= −1, which of the following could be true? ...
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No.18: (a + b*)* = ...
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No.19: If (2 - x)* = (x − 2)*, then x = ?...
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Total Questions: 19
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