MHB Prove that function is invertible

[Nath1]

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

 

[Opalg]

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 $.