The operation # is defined for all nonzero x and y by x#y=x+. If a>0, then 1#(1#a)=

[x] is the greatest integer less than or equal x, what is the value of []+[]+[]?

Let x∗∗∗=x−x² for all non-negative integers x. Which of the following equals x²−x+x∗∗∗?

a∘b= for all a, b that satisfy a≠−b. What is the value of (–4)∘2?

If f(x)=2x⁴−x², what is the value of f()?

For all numbers x and y the definition of the operation ♦ is x♦y=xy(x+4). If (−6)♦a=−60, then what is the value of a ?

Define x* by the equation x* = π – x. Then ((–π)*)* =

Life expectancy is defined by the formula , where S = shoe size, B = average monthly electric bill in dollars, and G = GRE score. If Melvin’s GRE score is twice his monthly electric bill, and his life expectancy is 50, what is his shoe size?

If a♯b=, where b≥0, what is the value of (–4)♯4?

For any real number x, the operator & is defined as:

&(x) = x(1 − x)

If p + 1 = &(p + 1), then p =