If f(x).f(1/x) = f(x) + f(1/x) and f(4) = 65,
what will be the value of f(6) ?
Any help would be greatly appreciated.
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Now if is a homogeneous function, then . Thus (2)
Now use (1) and (2).
Originally Posted by Curious_eager If f(x).f(1/x) = f(x) + f(1/x) and f(4) = 65,
what will be the value of f(6) ? The answer could be almost anything, since the given information only determines the values of the function at x=4 and x=1/4. Probably the simplest function to satisfy the functional equation is , which would make .
If it's a homogeneous function you don't even need to go through all the steps that I showed since you can just use the fact that and
Try posting the question exactly as it was given.
The question actually is that :
If is a polynomial function satisfying the condition that
and .Then what is value of .
On assuming a poloynomial of degree and plugging it in the given condition and equating the coefficients we get
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