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Prove that f: R->R , given by f(x)=2x , ...

Prove that `f: R->R` , given by `f(x)=2x` , is one-one and onto.

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The function is one-to-one if every element of the
codomain is mapped to by at most one element of the domain
The function is onto if every element of the codomain is
mapped to by at least one element of the domain
`f(x)=2x`
Domain of f =Codomain of f = R
Every element of r(codomain) is mapped to only one element in R(domain)
i.e. `f(x)=f(y)`
`⟹2x=2y⟹x=y`
...
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