perplexus.info :: Just Math : Find the Function 2

Find the Function 2 (Posted on 2025-04-06)

Find the function f(x), where:
f: R→R, and:
f(x+y)-f(x-y) = f(x)*f(y)

No Solution Yet Submitted by K Sengupta

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Some thoughts

Comment 1 of 1

Let y = 0

Then f(x) - f(x) = f(x)*f(0)

so 0 = f(x)*f(0)

so f(0) = 0

Let y = x

then f(2x) - f(0) = f(x)*f(x)

so f(2x) = f(x)*f(x)

This implies that f(x) = a^x

But f(0) = 0, which seems like a contradiction.

The only function that I can figure out that works is f(x) = 0

Posted by Steve Herman on 2025-04-08 09:15:52

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