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If (2 - x)* = (x − *, then x.   

If (2 - x)* = (x − 2)*, then x = ?
(A) 0
(B) ...
(C) ...
(D) ...
(E) ...

*This question is included in Nova Math - Problem Set D: Defined Functions

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Posted: 10/20/2012 00:41
Why does (x-2) become 2-(x-2) and not (2-x)-2? I thought I needed to replace x with (2-x) but in the solution presented that doesn't seem to be the case.
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Posted: 10/22/2012 13:06
Mona, in questions like these, think of (..)* as ƒ(x). So x*=ƒx) = 2 - x. We don't replace x with 2-x. We replace whatever is in the parentheses with 2 - whatever is in the parentheses.

That means (2-x)*=ƒ(2-x)= 2 - (2-x), and (x-2)* = ƒ(x-2) = 2 - (x-2). And 2 - (2-x) = 2 - (x-2). Now you can solve it.

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