Finding Global Inverse of $ f(x,y,z)= \left( \frac{x}{a+x+y+z}, \frac{y}{a+x+y+z}, \frac{z}{a+x+y+z} \right).$
Proving $f(x,y,z)=\big(\frac{x}{a+x+y+z}, \frac{y}{a+x+y+z}, \frac{z}{a+x+y+z} \big)$ is injective