Question

Let f(x) be a real valued function not identically equal to zero such that f(x+yn)=f(x)+(f(y))n; y is real, n is odd and n >1 and f'(0) ³ 0. Find out the value of f '(10) and f(5).

Joshi sir comment

take x = 0 and y = 0 and n = 3

we get f(0) = f(0) + f(0)n or f(0) = 0

now take x = 0,  y = 1 and n = 3

so f(1) = f(0) + f(1)3

so get f(1) = 1, other values are not excetable because f(x) be a real valued function not identically equal to zero and f'(0) ³ 0

similarly get the other values 

you will get f(5) = 5

so f(x) = x generally then find f (x) , i think it will be 1 

Submit Your Answer


please login to submit your answer

Login Here

Register