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Let N+N^+N+ be the set of positive integers and f:N+→N+f:N^+\rightarrow N^+ f:N+→N+ be a mapping defined by f(x)=2x,x∈N+f(x)=2x, x\in N
Question

Let N+N^+ be the set of positive integers and f:N+N+f:N^+\rightarrow N^+  be a mapping defined by f(x)=2x,xN+f(x)=2x, x\in N^+. Then mapping ff is​

A.

injective

B.

surjective

C.

neither injective nor surjective

D.

bijective

Correct option is A

Given: f:N+N+,f(x)=2xInjective:f(x1)=f(x2)=>2x1=2x2=>x1=x2=>InjectiveSurjective:Range of f={2,4,6,8, }N+Odd numbers like 1,3,5, are not in the range=>Not surjectiveFinal Answer: (A) Injective\textbf{Given: } f: \mathbb{N}^+ \to \mathbb{N}^+, \quad f(x) = 2x \\[6pt]\textbf{Injective:} \\f(x_1) = f(x_2) \Rightarrow 2x_1 = 2x_2 \Rightarrow x_1 = x_2 \Rightarrow \text{Injective} \\[6pt]\textbf{Surjective:} \\\text{Range of } f = \{2, 4, 6, 8, \dots\} \subset \mathbb{N}^+ \\\text{Odd numbers like } 1, 3, 5, \dots \text{ are not in the range} \\\Rightarrow \text{Not surjective} \\[6pt]\boxed{\text{Final Answer: (A) Injective}}​​

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