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Functional Finding (Posted on 2023-12-24)

Determine all f(x) on reals excluding zero such that

(1/x)f(-x) + f(1/x) = x

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

| Comment 2 of 3 |

(1/x)f(-x) + f(1/x) = x

replacing x with -x

-f(x)/x + f(-1/x) = -x

multiply by -x:

f(x) - x*f(-1/x) = x^2 eqn 1

replacing x with 1/x

x*f(-1/x) + f(x) = 1/x eqn 2

Adding eqns 1 and 2 gives

f(x) = (1/2)(x^2 + 1/x)

f(x) = (x^3 + 1)/(2x)

(same solution as paul)

Edited on December 24, 2023, 2:56 pm

Posted by Larry on 2023-12-24 14:55:35

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