Discussion
If (2 - x)* = (x − 2)*, then x = ?
*This question is included in Nova Math - Problem Set D: Defined Functions, question #19
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| (B) | ... |
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| (D) | ... |
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The solution is
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.
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.
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.