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Re: Algebra 2/Trig Regents
Posted:
Jun 22, 2011 9:52 AM
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What is even more sad... is shouldn't be referred to as "an argument"-
rather is should be a collaborative conversations about a problem, in
which the solution is based sole on what is best for students!
Susan L. Rothwell, Mathematics Coordinator
Staff & Curriculum Development
From: Nick B <nbianculli@gmail.com>
To: nyshsmath@mathforum.org
Date: 06/22/2011 01:07 AM
Subject: Re: Algebra 2/Trig Regents
Sent by: owner-nyshsmath@mathforum.org
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
multi-valued 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.
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