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