Q. 14.8( 4 Votes )

# Mark (√) against the correct answer in the following:

f : N → N : f(x) = 2x is

A. one - one and onto

B. one - one and into

C. many - one and onto

D. many - one and into

Answer :

f(x) = 2x

For One - One

f(x_{1}) = 2x_{1}

f(x_{2}) = 2x_{2}

put f(x_{1}) = f(x_{2}) we get

2x_{1} = 2x_{2}

Hence, if f(x_{1}) = f(x_{2}), x_{1 =} x_{2}

Function f is one - one

For Onto

f(x) = 2x

let f(x) = y, such that y∈N

2x = y

⇒

If y = 1

x =

which is not possible as x∈N

Hence, f is not onto., f is into

Hence, option b is correct

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