## Discussion

If ((1 –

*This question is included in Nova Math - Diagnostic/Review:, question #30

*x*)*)* = (1 –*x*)*, then*x*=(A) | 1/2 |

(B) | ... |

(C) | ... |

(D) | ... |

(E) | ... |

(F) | ... |

The solution is

Posted: 03/21/2012 00:40

Why did the * in the second step disappear and a 1 appear ?

Posted: 04/07/2012 14:59

Yes, don't understand either....why is 1 being substituted for *

This is the strangest thing I have ever seen and the explanation is not very clear I would very much like a better explanation.

Hi guys, in "defined functions" problem like this, think of any symbol like * here that defines a function as ƒ(..). So, think of x* as ƒ(x), which in this case, ƒ(x) = 1-x

Let's work on the left hand side of the equation first.

(1-x)* = ƒ(1-x) = 1 - (1-x) = 1 - 1 + x = x

So, ((1-x)*)* = (x)* = ƒ(x) = 1-x.

Now, let's work on the right side. But we already did that. (1-x)* = x.

Hence, we have: 1-x = x, and so x = ....

I hope that helps.

Let's work on the left hand side of the equation first.

(1-x)* = ƒ(1-x) = 1 - (1-x) = 1 - 1 + x = x

So, ((1-x)*)* = (x)* = ƒ(x) = 1-x.

Now, let's work on the right side. But we already did that. (1-x)* = x.

Hence, we have: 1-x = x, and so x = ....

I hope that helps.

Posted: 04/15/2012 07:51

It really helps, thanks!

Posted: 02/01/2017 09:38

Reply:

Thank you Vicki for the acknowledgment. If you have a moment, please rate the app in the App Store. We appreciate it.

Posted: 05/16/2012 18:01

How does (1-x)*= 1-(1-x)?

Tiffany, thanks for your question. I explained this pretty thoroughly (please look at earlier / above explanations). To repeat:

x* or ƒ(x) is defined as 1 - x. So, you substitute any variable, whether it's x, n, 1, a, M+1, y-5, etc. that has the * into the x in 1 - x.

In this case, for (1-x)* or ƒ(1-x), plug in 1-x into the x of the function.

So you have 1 - (1 - x).

x* or ƒ(x) is defined as 1 - x. So, you substitute any variable, whether it's x, n, 1, a, M+1, y-5, etc. that has the * into the x in 1 - x.

In this case, for (1-x)* or ƒ(1-x), plug in 1-x into the x of the function.

So you have 1 - (1 - x).

Posted: 05/16/2012 18:35

Oh I see it now thanks very much!

Tiffany, as Grandpa Oei would have said: kam sia lu, for the acknowledgment. If you have a moment, please rate the app in the App Store.

If x* = 1 - x

And

((1 - x)*)* = (1 - x)*

Then

((x*)*)* = (x*)*

x^3* = x^2*

x* = 1

(x*)^(1/*) = 1^(1/*)

x = 1

The statement defining the problem defines the symbol *. It does not define the function. Therefore, equating x* to f(x) is incorrect. Perhaps that is intended, but nonetheless it is incorrect.

And

((1 - x)*)* = (1 - x)*

Then

((x*)*)* = (x*)*

x^3* = x^2*

x* = 1

(x*)^(1/*) = 1^(1/*)

x = 1

The statement defining the problem defines the symbol *. It does not define the function. Therefore, equating x* to f(x) is incorrect. Perhaps that is intended, but nonetheless it is incorrect.

Mike, you can't just raise x to the power of 3 or 2 just because x is operated on by the symbol * 3 or 2 times. Trust me, it is easier to think of it like f(x). If you don't understand it then you need to review the chapter on functions.

With defined function, why don't we distribute the symbol * as we'd do with other variables. Seen on the left side equation (1-x)* becomes (1- x*) which equals, (1 - (1-x). But why don't we distribute the * to the 1 so it becomes, ( *-x*). This is we're it becomes unclear.

Posted: 01/26/2013 13:12

How (1-x)* can be equal to 1-x*?

Posted: 04/12/2013 02:16

Love the app

Posted: 04/16/2013 19:18

Hello Mac. We love the students.

Posted: 11/13/2013 20:34

This is beyond confusing. I have no idea where to start.

Scott, Joel Brainer explained this in the thread. Here I repaste his answer:

Hi guys, in "defined functions" problem like this, think of any symbol like * here that defines a function as ƒ(..). So, think of x* as ƒ(x), which in this case, ƒ(x) = 1-x

Let's work on the left hand side of the equation first.

(1-x)* = ƒ(1-x) = 1 - (1-x) = 1 - 1 + x = x

So, ((1-x)*)* = (x)* = ƒ(x) = 1-x. (Substitute x into (1-x)* since we just established that.)

Now, let's work on the right side. But we also did that. (1-x)* = x.

Hence, we have: 1-x = x, and so x = ....

Hi guys, in "defined functions" problem like this, think of any symbol like * here that defines a function as ƒ(..). So, think of x* as ƒ(x), which in this case, ƒ(x) = 1-x

Let's work on the left hand side of the equation first.

(1-x)* = ƒ(1-x) = 1 - (1-x) = 1 - 1 + x = x

So, ((1-x)*)* = (x)* = ƒ(x) = 1-x. (Substitute x into (1-x)* since we just established that.)

Now, let's work on the right side. But we also did that. (1-x)* = x.

Hence, we have: 1-x = x, and so x = ....

Posted: 12/08/2013 22:20

I think 1^* is undefined.

Mohammed, sorry for the confusion. There is no exponential or power function in the statement. There is no 1^*. x* is defined as 1-x. So if you meant 1*, it is 1-1 or 0.

Posted: 03/27/2014 16:48

Cali, the definition is 1-x, not x-1

Posted: 10/13/2016 08:20

(1-x)^*=[1-(1-x)]^*???

So (1-x)^2=1-x^2?????

So (1-x)^2=1-x^2?????

And if * = x-1, then wouldn't RHS be: (x-1)(x-1)(x-1)?