Is the function from N×N\mathbb{N}\times\mathbb{N} to N\mathbb{N} which maps (n,m)(n,m) to 2n⋅3m2^n\cdot 3^m injective?

Where the function is not injective can we restrict it

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Is the function from N×N\mathbb{N}\times\mathbb{N} to N\mathbb{N} which maps (n,m)(n,m) to 2n⋅3m2^n\cdot 3^m injective?

Where the function is not injective can we restrict it

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