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Questions tagged [inverse]

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34 votes
5 answers
6k views

Why are there two inverses to exponentiation?

I'm not sure if this is more educational or more "pure math", but: For multiplication and addition, there is exactly one inverse operation, namely division and subtraction. For ...
Jasper's user avatar
  • 2,699
13 votes
2 answers
3k views

Logarithm Tables - How were the values reached?

I'm teaching an Algebra II/Trigonometry class that is currently working on logarithms as the inverse function of exponential functions. Now, to keep their interest I had them struggle for a few ...
Jhecht's user avatar
  • 263
8 votes
9 answers
1k views

Method of Solving $5^x=326$ (Logs not allowed)

$5^x=326$ A book titled "algebra and trigonometry" by Paul Foerster, offers this problem. It came before the logarithm chapter and specifically said not to solve with any log manipulation. It ended ...
JTP - Apologise to Monica's user avatar
8 votes
3 answers
1k views

What are some common ways students get confused about finding an inverse of a function?

What are some common ways students get confused about finding an inverse of a function? One I can think of is conflating multiplicative inverses of rational numbers with functional inverses. e.g. ...
Eleanor Hankins's user avatar
7 votes
1 answer
293 views

Why many people believe that: $\displaystyle c>0\implies \frac{1}{c}<0$?

I came across many people who believe the below false implication. I don't know why people believe it true in high school and middle school and also students in university level. Really I would like ...
zeraoulia rafik's user avatar
7 votes
2 answers
390 views

Why bother calculating the inverse of 3 by 3 matrix?

My government has told me that I must teach 17 year olds how to invert a 3 by 3 matrix using adjoints/cofactors, without using any technology. Is there any reason why you would want to know how to do ...
Jezza Judge's user avatar
6 votes
3 answers
2k views

Apply the inverse operation on both sides, or know the inverse function?

My old question here was about logarithms, but as I teach more and more (precalculus) algebra, I've generalized the question a bit in my mind. Should students do the same thing to both sides, or ...
Chris Cunningham's user avatar