MHB Prove that function is invertible

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The function ${2}^{n}(2n+1)-1$ is proposed for proof of invertibility from $\Bbb{N} \times \Bbb{N}$ to $\Bbb{N}$. To establish invertibility, the function must be shown to be both injective and surjective. A participant suggests that the function may need two distinct variables for clarity, possibly indicating a typographical error in the original formulation. The discussion emphasizes the importance of correctly interpreting the function's variables to proceed with the proof. Clarification on the function's structure is essential for further analysis.
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prove that the function

${2}^{n}.(2n+1)-1 $ from $ \Bbb{N}$x$\Bbb{N}\implies\Bbb{N}$
is invertible

I know that a function to be invertible must be injective and surjective, I am not sure how to calculate this since in this case I need a pair (x,y) since the function comes from $ {\Bbb{N}}^{2}$.

Can anyone help me ? thanks
 
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Nath said:
prove that the function

${2}^{n}.(2n+1)-1 $ from $ \Bbb{N}$x$\Bbb{N}\implies\Bbb{N}$
is invertible

I know that a function to be invertible must be injective and surjective, I am not sure how to calculate this since in this case I need a pair (x,y) since the function comes from $ {\Bbb{N}}^{2}$.

Can anyone help me ? thanks
Hi Nath, and welcome to MHB!

I think you need to double-check that you have read the question correctly. It only makes sense if there are two different variables in the function, perhaps ${2}^{\color{red}m}.(2n+1)-1 $.
 
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