Math CentralQuandaries & Queries


Question from Dana, a student:

Find a function t(x) such that t(x)/x+3 = y is an even function

Hi Dana,

Are you given any other information? If there are no other restrictions there is a simple (trivial) answer: Just let t(x) = x + 3. Then y = (x+3)/(x+3) = 1, which is an even function of x.

Extending on this idea, you could design t(x) to be a product of (x+3) and any even function. Then you get:

t(x)/(x+3) = (x+3)[even function] / (x+3) = [even function]


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