Define x* by the equation x* = π-x. Then ((−π)*)* =

Question

Define x* by the equation x* = π-x. Then ((−π)*)* = (A) −2π (B) -1 (C) −π (D) 2π (E) 4π I've attached a picture of a function problem example to this post. It even explains two ways to solve it but I still don't understand. Without having to re-learn some basic math that I must be missing is there a fast way to eliminate answer choices or estimate in a way that will help me test day? :oops:

Question: Define x* by the equation x* = π – x. Then ((–π)*)* = Screen Shot 2016-09-06 at 12.05.57 pm.png

wainsdaylion · Answer

Isabelle,

This is relatively straight forward algebra. What part of the question / answer are you having trouble understanding?

IsabelleTreuille · Answer

Thank you so much for replying!

In the second way to solve:
f(f(−π)) = f(π − (−π)) = f(π + π) = f(2π) = π − 2π = −π.

I don't understand at all how we get from
this: f(f(−π)) 
to this: f(π − (−π))
to this: f(π + π)

Also, I don't usually see explanations turning unknown function questions into classic 'functions' with f(x) - do you know if there is a reason why this is?

Bunuel · Answer

Check function questions in our Special Questions Directory : Operations/functions defining algebraic/arithmetic expressions Symbols Representing Arithmetic Operation Rounding Functions Various Functions Hope it helps. P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you.

wainsdaylion · Answer

"this: f(f(−π))
to this: f(π − (−π))"

Ignore the wrapper function (the extra f() ) for a moment...

The function is f ( x ) = π - x, so
f ( π ) = π -  x  -π
f ( π ) = π - ( - π )

Is that any clearer? If so...subtracting a negative is the same as adding.
π - ( - π ) = π + π

Why is there a question using an unusual function format instead of the standard f()? I do not question the why of GMAT! But I suspect it's testing your mental flexibility, that you grasp we're just dealing in symbols that we can arbitrarily define and that x* has nothing to do with the multiplication or exponential functions but is simply a function we're newly defining.

Usernamevisible · Answer

Given:
x* = π - x

Find:
((−π)*)*

Step 1:
(−π)* = π - (−π) = π + π = 2π

Step 2:
(2π)* = π - 2π = −π

Final Answer:
−π

Define x* by the equation x* = π-x. Then ((−π)) =

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