I understand that given two functions f:X→Y and g:Y→X, to say that f is the inverse function of g means g o f:X→X is defined by g(f(x))=idx and to say g is the inverse function of f means f o g: Y→Y is defined by f(g(x))=idy I understand how to find inverses of one variable functions and I'm able to apply this definition. However I'm having difficulty of finding examples of finding inverses of maps such as f:ℝ^2→ℝ^2 or something like f:ℝ^3→ℝ^3. Similarly I'm not sure if we can find inverses of functions with such mappings as f:ℝ^2→ℝ. Specific examples would highly be appreciated. Thanks.