Extra functions strategy

[ysabelle1984]

Hello.

I am currently reviewing the chapter 10, section Symmetry of the MGMAT Algebra. At the beginning of that section, the problem asks to find the function for which f(x)= f(1/x).

The answer is listed as B. However when I do the calculations, I see that f(x) yields a result of 2, whereas f(1/x) yields a result of -2. In the book it says that (1/3+1)/(1/3-1)=2 but shouldn't that be -2? How come the negative sign disappears when you flip the fraction?

Or should it be interpreted as in function problems, the sign doesn't matter as long as the number is the same?

Thank you!

[RonPurewal]

Hello.

I am currently reviewing the chapter 10, section Symmetry of the MGMAT Algebra. At the beginning of that section, the problem asks to find the function for which f(x)= f(1/x).

The answer is listed as B. However when I do the calculations, I see that f(x) yields a result of 2, whereas f(1/x) yields a result of -2. In the book it says that (1/3+1)/(1/3-1)=2 but shouldn't that be -2? How come the negative sign disappears when you flip the fraction?

Or should it be interpreted as in function problems, the sign doesn't matter as long as the number is the same?

Thank you!

Look at the book again. All of those functions have absolute value bars around them, so the results are all non-negative.

Ironically, because there are so many absolute value bars everywhere, it seems that you're just forgetting about them. Maybe psychologically they just became part of the "environment", at least as far as this problem is concerned.

[ysabelle1984]

Thanks Ron you are absolutely right! How did I miss these? ;)

Thanks!

[RonPurewal]

Thanks Ron you are absolutely right! How did I miss these? ;)

Thanks!

Ironically, it's probably the fact that there are so many of them. They just start to become "background".

Just remember to pay attention to such things (= symbols that are repeated over and over and over and over) should you encounter them on the real exam.