Define $f(x,y,z)=x^2y+e^x+z$. Show that there exists a differentiable function $g(s,t)$ in some neighborhood of (1,-1) in $R^2$, such that $g(1,-1)=0$ and $f(g(y,z),y,z)=0$!
I am trying to do the above but have problem with the differentiable function of $g(s,t)$ which is not match with the variables in $f(x,y,z)$? So any help for solving this problem is appreciated.