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

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

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Solution: We observe the following properties of f:

Injectivity:Let  \ x1,x2in R such that \ f(x1)=f(x2) .then ,

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

So , \ f:R ightarrow Ris one -one

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

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

Posted by

Deependra Verma

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