MathLabs

Problem 4

Construct a function f:Q+→Q+f:\mathbb Q^+\to\mathbb Q^+ such that f(xf(y))=f(x)/yf(xf(y))=f(x)/y for all positive rational numbers x,yx,y.
Step 3 of 5: Derive the reciprocal relation
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f(f(x))=1xf(f(x))=\frac1x
Detailed analysis

Set x=1 in the original equation and use f(1)=1: f(f(x))=f(1)/x=1xf(f(x))=f(1)/x=\frac1x.