Question

Considerando f: R* → R, tal que f(2)=1 e f(a.b) = f(a)+f(b), calcule:

f(1)=


f(4)=


f(8)=

Answer 1

Parece simples....

f(a.b)=f(a)+f(b)
f(2.1)=f(2)+f(1)=1   conforme enunciado, f(2)=1

Logo 1+f(1)=1   →   f(1)=0
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f(2.2)=f(2)+f(2)
f(4)=1+1
f(4)=2
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f(4.2)=f(4)+f(2)
f(8)=2+1
f(8)=3

:-)