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Nova Math - Problem Set C: Defined Function
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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 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 . Then 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 . For what values of a does ? ...
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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 tru...
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No.8: The operation * is defined for all non-zero x and y by the equation x * y = x/y. Then the expression...
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No.9: Let . For what value of x does 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: If , for all x, 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 for all positive x and y. Then ...
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No.14: is a function such that 1 a = 1 and a b = b a for all a and b. Which of the following must be tru...
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No.15: The symbol denotes one of the operations: addition, subtraction, multiplication, or division. Furth...
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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?   I. x = y  II. x > y I...
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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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