# Mark (√) against the correct answer in the following:f : N → N : f(x) = 2x isA. one - one and ontoB. one - one and intoC. many - one and ontoD. many - one and into

f(x) = 2x

For One - One

f(x1) = 2x1

f(x2) = 2x2

put f(x1) = f(x2) we get

2x1 = 2x2

Hence, if f(x1) = f(x2), x1 = x2

Function f is one - one

For Onto

f(x) = 2x

let f(x) = y, such that yN

2x = y If y = 1

x = which is not possible as xN

Hence, f is not onto., f is into

Hence, option b is correct

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