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.