Show that f(rx)=(f(x))^r for all r in QQ if f(x+y)=f(x).f(y) for all x,y in RR

Danika Mckay

Danika Mckay

Answered question

2022-10-29

f : R R be function satisfying f ( x + y ) = f ( x ) . f ( y ) for all x , y R and l i m x 0 f ( x ) = 1 then show that f ( r x ) = ( f ( x ) ) r for all r Q

Answer & Explanation

Pradellalo

Pradellalo

Beginner2022-10-30Added 16 answers

( f ( x q ) ) p = ( f ( x q ) ) q r = ( f ( x ) ) r
since f ( x ) = f ( x q + x q + + x q ) = f ( x q ) q

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