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Define a @ b to be a3 – 1.  What is the value of x @ 1 ?
(A)0
(B)...
(C)...
(D)...
(E)...
(F)...
*This question is included in Nova Press: Problem Solving Diagnostic Test, question #29

The solution is

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Contributor
Posted: 11/17/2011 09:24
Is there a mistake in this question? It doesn't make sense.
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Contributor
Posted: 11/17/2011 11:53
Zoe, Yes, there is a mistake here. The question is supposed to read: Define a @ b to be a^3 - 1 (a to the power of 3, minus 1). Then it makes sense. Please try again.
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Contributor
Posted: 11/17/2011 12:10
Yep. That's a typographical error alright.

We'll fix that for the next update.
Posted: 03/24/2012 19:16
I do not understand. What means: a@b and x@1?
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Contributor
Posted: 03/24/2012 20:07
Beverly, here is a way to think about @ and "defined functions" questions: in a function involving a and b, where the function is defined as a^3 - 1, what if a is substituted with x, and b with 1? The math notation is attached. Hope this helps.
Posted: 11/17/2015 08:12
Reply: sorry...could you please make the notation more clearly...I cannot understand..
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Admin
Posted: 11/17/2015 13:30
Hi Freya,

The problem is an exercise in notation. It is testing your ability to understand unusual structures.

Let's rewrite the the problem using standard function notation:

f(a) = a^3 - 1

Notice that we did not include the b in the function because it does not appear in the definition a^3 - 1. (If you are familiar with functions of 2 variables, then the function could be written as f(a, b) = a^3 - 1)

Now, to calculate f(x) or f(x, 1), we merely replace the a in the in the function f(a) = a^3 - 1 with x:

f(x) = x^3 - 1

The key to this problem is to realize how simple it is: The notation is merely asking you to replace the a in a^3 - 1 with x.

Note: Although the problem is simple, it would be consider to a hard problem (probably very hard) on the test because most students would get it wrong.
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