> 
> If $f(x,y)$ is a continuous on the $\mathbb{R}^2$, please show that $\exists g$ where $g$ is an injective function, and
> 
> 
> $$g:\mathbb{R} \to\mathbb{R}^2
> \quad s.t. \quad 
> f\circ g= \text{ constant}.$$
> 
> 
> 

This is a test of my entrance exams. I haven't thought about it for a long time. I hope you can give me some advice.

Thank you.