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Question Number 56921 by rahul 19 last updated on 26/Mar/19

$$Given:$$$$f\left(xy\right)=f\left(x\right).f\left(y\right)\mathrm{\forall }x,yϵ\mathbb{R}andf\left(0\right)\ne 0$$$$thenf\left(x\right)=?$$

Answered by mr W last updated on 26/Mar/19

$$f\left(xy\right)=f\left(x\right)f\left(y\right)$$$$withy=0$$$$f\left(0\right)=f\left(x\right)f\left(0\right)$$$$sincef\left(0\right)\ne 0\Rightarrow f\left(x\right)=1$$

Commented by rahul 19 last updated on 26/Mar/19

$$Sir,howtofindvalueofnifweassumed$$$$f\left(x\right)=x^n?$$

Commented by mr W last updated on 27/Mar/19

$$f\left(x\right)\ne x^n,sincef\left(0\right)\ne 0.$$$$f\left(x\right)=1istheonlyonesolution.$$

Commented by rahul 19 last updated on 27/Mar/19

thank you sir!

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