I don't understand what * is supposed to mean. Is it supposed to be a power function? I don't understand the substitution in the solution.

Hi Angie,

The * is an operator.
So whenever you see x*, you have to sub in 1 - x. (As the problem says, x will always be non-negative for this operator.)

So if you have 6*, that's equal to 1 - 6., which is -5.

Now for the actual problem:

As you can see, the left-hand side of the problem has two *'s. Let's simplify that side by take each * on one at a time.

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

Let's clean it up a bit:
((1 - 1 + x))* =
((x))* =

You can see here we've gotten rid of one of the *'s. Now for the other:
x* =
1 - x

So the left-hand side simplifies to 1 - x.

Now for the right-hand side:
(1 - x)* =
1 - (1 - x) =
1 - 1 + x =
x

Let's put 'em together (left-hand side & right-hand side):
1- x = x
1 = 2x
1/2 = x

Hope that helps.

That was quick. I just downloaded this app and was trying the free sample questions. This one got me stuck. Thanks for the explanation. I missed that * is an "operator". I am liking this discussion board already.

I don't understand the 2nd step lhs

The second step is simplifying the expression using the commutative property of addition. This property means that numbers can be added in any order and the sum will be the same.

((1 - (1 - x))*
((1 - 1 + x))* = (distribute negative sign and then remove inner parentheses)
((x))* = (subtract 1 from 1)
x* (remove all parentheses)

It's always a good idea for the math section of these tests to be rock solid on the order of operations: PEMDAS (you may have learned this acronym with the mnemonic "Please Excuse My Dear Aunt Sally). The order of operations is Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Of course, multiplication and division are interchangeable, as are addition and subtraction, but it is helpful to have a go to order for every algebraic expression.

In addition, the newly defined function (or "made-up function" as I like to call it) is a common problem type, one that every test taker should, and can, master. This particular problem is especially tricky because the made-up function (*, or "asterisk") looks an awful lot like the multiplication symbol.

Why doesn't the * cancel out on both sides to leave you with (1-x)* = 1-x

The symbol, *, is a function operator so it cannot be cancelled out. Similarly, you cannot cancel out the addition symbol, +, in an equation. Again, the test makers made this whole problem potentially more confusing because the new symbol looks like the multiplication operator. More often, however, they use other symbols, such as diamonds, boxes, and the like.

In these types of problems, where the test maker introduces a new function operator, the only way to remove it so that you are left with the "normal" operations (addition, subtraction, multiplication, division, etc.) is to substitute the new operator with it's definition.

The definition of the new operator, *, basically says this: "take everything on the left of the * and subtract it from 1."

In your question, Bryan, you ask about (1-x)*. Everything to the left of the * is (1-x), so,using the definition above, we subtract this from 1:

1-(1-x)

The * is now removed and we can do our normal arithmetic on the result:

1-(1-x )= 1-1+x = x

Hope that answers your question!

Looks too much like it's supposed to be a power, like (1-x)* = (1-x)^(1-x)

Probably should find a way to make that more clear.

But, for example:
(X-1)^2= (x-1).(x-1) not equal to:
(X^2-1^2), which is what you guys are impliying?????

But, for example:
(X-1)^2= (x-1).(x-1) not equal to:
(X^2-1^2), which is what you guys are impliying?????