Math CentralQuandaries & Queries


Question from Joan, a teacher:

Let f be a function satisfying f(x) + 2f(1/x) = x for all real numbers (x does not equal 0)
a) Find f(1) justify your answer

b) Find f(2) justify your answer

Hi Joan,

For part a) substitute x = 1 in the expression

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

to get

f(1) + 2f(1) = 1

Solve for f(1).

This technique doesn't work for part b) since substitution of x = 2 yields

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

Which is one equation in two unknowns, f(2) and f(1/2). To solve for f(2) you need a second equation containing f(2) and f(1/2), What happens when you substitute x = 1/2 into the defining equation?


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