f(2n)= 2f(n) for all in integers n
f(4) =4
IF f is a function defined for all positive integers n, and f satisfies the two conditions above, which of the following could be the definition of f?

Question

f(2n)= 2f(n) for all in integers n
f(4) =4
IF f is a function defined for all positive integers n, and f satisfies the two conditions above, which of the following could be the definition of f?

anonymous · Answer

let n=2 

f(4)=2f(2)
4=2f(2)
f(2)=2

let n=1

f(2)=2f(1)
2=2f(1)
f(1)=1
...............................
it seems$$f(n)=2^{n-1}$$is an answer...we prove by induction
$$f(1)=2^{1-1}=1$$$$f(n+1)=2f(n)=2\times 2^{n-1}=2^n$$

anonymous · Answer

so $$f(n)=2^{n-1}$$must be one of ur options