Problem 3 Given m∈Nm\in\mathbb{N}m∈N . Find all functions f:R+→R+f:\mathbb{R^{+}}\rightarrow\mathbb{R^{+}}f:R+→R+ such that f(f(x)+y)−f(x)=(f(y)y−1)x+fm(y)f(f(x)+y)-f(x)=\left( \frac{f(y)}{y}-1\right)x+f^m(y)f(f(x)+y)−f(x)=(yf(y)−1)x+fm(y) holds for all x,y∈R+.x,y\in\mathbb{R^{+}}.x,y∈R+. ( fm(x)=f^m(x) =fm(x)= fff applies mmm times.)