help in finding a function

You need to supply a function in order to talk about the inverse to that function
 
it is easy to find a function, and it is easy to prove if it inverse function or not, but my problem is to find an inverse function...
 
itay sason said:
it is easy to find a function, and it is easy to prove if it inverse function or not, but my problem is to find an inverse function...
Click to expand...

I don't think you know what "inverse function" means. Perhaps you mean invertible function
 
ok so invertible i don't think it matter,but then again my language isnt english. i want a function f : R^2->R, that f^(-1) exist. i dont think i need to explain what is f^(-1)
 
itay sason said:
ok so invertible i don't think it matter,but then again my language isnt english. i want a function f : R^2->R, that f^(-1) exist. i dont think i need to explain what is f^(-1)
Click to expand...

A function that has an inverse is called invertible. It is also referred to as injective (or bijective if you require also the entire range also be hit).

Try \(\displaystyle f: (0.x_1x_2x_3x_4..., 0.y_1y_2y_3y_4...) \mapsto 0.x_1y_1x_2y_2x_3y_3...\), where these are the base-10 (or other) representations

This maps \(\displaystyle [0,1)\times [0,1)\to [0,1)\). Show it has an inverse on this domain and range.

Now can you find invertible \(\displaystyle g:\mathbb{R}^2\to [0,1)^2\) and \(\displaystyle h:[0,1)\to \mathbb{R}\)?

If you can then: \(\displaystyle F = h\circ f\circ g\) will work.
 
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