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

Solution: We observe the following properties of f:

Injectivity:Let  $\\ x1,x2\in R$ such that $\\ f(x1)=f(x2)$ .then ,

$\\ f(x1)=f(x2)\\ \\\Rightarrow 2x1=2x2\\ \\\Rightarrow x1=x2$

So , $\\ f:R\rightarrow R$is one -one

Surjectivity: Let y be any real number in R(co-domain) then

Clearly, $y/2\in R;for;y\in R$ such that $f(y/2)=2y/2=y$

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