Discussion
Define a @ b to be a3 – 1. What is the value of x @ 1 ?
*This question is included in Nova Press: Problem Solving Diagnostic Test, question #29
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The solution is
Posted: 11/17/2011 09:24
Is there a mistake in this question? It doesn't make sense.
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.
Posted: 11/17/2011 12:10
Yep. That's a typographical error alright.
We'll fix that for the next update.
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?
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..
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.