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 1 of 5: Determine f of one
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f(1)=1f(1)=1
Detailed analysis

Putting x=y=1 gives f(f(1))=f(1)f(f(1))=f(1). Applying the original equation with x=1 and y=f(1), then using this equality, yields f(1)=1f(1)=1.