
Re: Algebra 2/Trig Regents
Posted:
Jun 22, 2011 12:58 AM



Here is an argument from both sides regarding #32:
On page 548 of the Math B textbook, there is a specific example given about function g and inverse relation g^1, which is not a function but uses the same notation that we are so used to seeing for an inverse function. This example pretty clearly states that if given function g, then inverse relation g^1 is not necessarily a function.
Maybe this is what NYS was referring to in answering teacher inquiries about #32.
On the flip side, the Amsco's A2/T book, which I assumed would be similar to this Math B book, does not repeat this exact example in its edition. Does this mean it was corrected for the new edition? In addition, every precalc or calc book that I have found states that g^1 is the notation for an inverse function, and that g^1 does not exist of g is not onetoone.
Jayson Kiang Mathematics Department Chairperson Longwood High School 631.345.9247 >>> 06/21/11 11:38 PM >>> Doesn't the school principal have the right to allow teachers to use their best judgement? In other words, if the teachers explain to the principal that question 32 is flawed and that the teachers would like to award full credit for various answers based on that, can't the principal give his/her permission? I'm pretty sure they can Liz Waite
Original Message From: Nick B To: nyshsmath Sent: Tue, Jun 21, 2011 10:18 pm Subject: Re: Algebra 2/Trig Regents
She's correct in saying that the inverse relation of a function may not be a function itself. Every function has a corresponding inverse relation; however, we usually say a function is invertible iff its inverse relation is a function. However, the question specifically asked to find f^1(x), which implies that the inverse relation is a function. After all, the letter f stands for function and any good book will define the notation f^1 to stand for the inverse function of f. So for the question to ask for an inverse function of f(x) = x^2  6 requires a domain restriction. If the question asked to find the inverse, then I could see her point but since the question specifically used the notation f^1(x), I completely agree with you.
In higher mathematics, there are such objects called multivalued functions, but we certainly don't study these concepts in any detail in high school.
The following Wikipedia article does the topic justice, and introduces multivalued inverses:
http://en.wikipedia.org/wiki/Inverse_function
It's the same concept in question 19. y = cos^1(x) denotes the inverse cosine FUNCTION, which is the inverse of y = cos x restricted to a domain of [0, pi].
What's sad is that we're the concerned, diligent math teachers who want to get it right and you bring a legitimate concern to light and are told that you won't "win the argument". At the minimum the question is ambiguous and poorly posed, regardless of whether SED thinks you didn't win the argument. What's even sadder is that this test is supposedly reviewed by trained eyes. How are mathematically educated people not picking up on these glaring errors and ambiguities? I saw the ambiguities within seconds of reading the questions (as I'm sure most all of us did) and somehow those questions ended up on the test. ******************************************************************* * To unsubscribe from this mailing list, email the message * "unsubscribe nyshsmath" to majordomo@mathforum.org * * Read prior posts and download attachments from the web archives at * http://mathforum.org/kb/forum.jspa?forumID=671 *******************************************************************

