I am encountering functions of real variable with the following property: $ f(x) = f(1/x) $ For example, $ f(x) = \left(x - \frac{1}{x}\right)\log^{3}{x} \qquad x > 0 $ Is there a name for this property?
Name that function property
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analysis
functions
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1@Shaun Ah, yes. You are correct. I thought of it as a function, rather than as a graph on 2-D. In any case, it might be best to say "$g(t)$ is an even function". – 2011-10-04
1 Answers
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Summary of comments:
- "Invariant under inversion" is a good name for such functions
- If the domain consists of positive numbers, one can say instead "$t\mapsto f(e^t)$ is even".