Define the symbol * by the following equation: x* = 1 − x, for all ... ...
Define the symbol * by the following equation: x* = 1 − x, for all non-negative x. If ((1 − x)*)* = (1 − x)*, then x =
(A) 1/2
(B) ...
(C) ...
(D) ...
(E) ...
*This question is included in
Nova Math - Diagnostic: Test / Review
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Posted: 12/30/2011 19:49
I don't understand the second step in the solution procedure. Please explain.
Contributor
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Posted: 12/30/2011 21:23
Muhammad, suppose 1-x is k and (1-x)*=k*
k*=1-k acc to the definition of the operator *
Substitute 1-x back for k, and you have 1-(1-x).
Contributor
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Posted: 12/31/2011 12:40
x*=muham + x
(mad)*=1
muham + mad = 1
That was just for fun.
I don't know whether Arcadia already helped you, if so, consider me just rambling on stuff you already know ;)
Technically you refer to the third line of the solution ergo (1-1+x)*=(1-x)* which is the second step in the solution.
Only the left side has changed here, from ( 1 - ( 1 - x ))* to ( 1 - 1 + x )*
If it would have been ( 1 + ( 1 - x ))* it would have solved into ( 1 + 1 - x )*
The difference is the leading minus sign, so we'll have to multiply each factor with negative 1 before being able to get rid of the parentheses.
-(whatever) ergo -1(whatever) becomes +(-whatever) get rid of parentheses make -whatever
You could also apply your newly acquired function/algorithm ergo the defined operator at once:
Given:
x* = 1 - x
We start with:
((1 − x)*)* = (1 − x)*
Solve all operators and we'll get:
1 - ( 1 - ( 1 - x )) = 1 - ( 1 - x )
Start to solve the leading minus signs from inner to outer parentheses to get rid of them all:
1 - ( 1 + ( -1 + x )) = 1 + ( -1 + x )
1 - ( 1 -1 + x ) = 1 -1 + x
1 +( -1 +1 - x ) = 0 + x
1 -1 +1 - x = x
1 - x = x
Subtract x on both sides:
1 - 2x = 0
Subtract 1 on both sides:
- 2x = - 1
Divide both sides by negative 2:
x = -1 / -2 ergo 1/2
x = 1/2 and that's our answer
Niels
Greetings from Holland
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Posted: 02/24/2012 22:32
i dont understand D: can someone explain
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Posted: 11/21/2012 14:18
The symbol is like a function. When given an equation/function, x*=1-x, whatever's within * will equal the left part of the first equation/function.
x*=1-x
(1-x)*=1-(1-x)
(1-x) on the second equation acts like x from the first equation.
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Define the symbol * by the following equation: x* = 1 − x, for all ... ...
Posted: 10/15/2014 08:27
How come nobody posts on here anymore?
Contributor
Reply 1 of 1
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Posted: 10/15/2014 11:27
Hi Minecraft Mineiac, the SAT test was just administered in September, so not many kids are studying for the test right now. You are getting a jump start.
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Define the symbol * by the following equation: x* = 1 − x, for all ... ...
Posted: 10/15/2014 08:28
✏️