A função f : R → R {\displaystyle f:\mathbb {R} \to \mathbb {R} } é tal que, ∀ x ∈ R , f ( 5 x ) = 5 f ( x ) e f ( 25 ) = 5 {\displaystyle \forall x\in \mathbb {R} ,f(5x)=5f(x){\mbox{ e }}f(25)=5}
5 = f ( 25 ) = f ( 5 ⋅ 5 ) = 5 f ( 5 ) ⇒ f ( 5 ) = 1 ⇒ 1 = f ( 5 ) = f ( 5 ⋅ 1 ) = 5 f ( 1 ) ⇒ f ( 1 ) = 1 5 {\displaystyle 5=f(25)=f(5\cdot 5)=5f(5)\Rightarrow f(5)=1\Rightarrow 1=f(5)=f(5\cdot 1)=5f(1)\Rightarrow f(1)={1 \over 5}}
