f: N rightarrow N, f(x) = x^3 is . . . . . . | vedclass

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(B) To determine if $f(x) = x^3$ is one-one and onto for $f: N \rightarrow N$:$1$. One-one check: Let $f(x_1) = f(x_2)$. Then $x_1^3 = x_2^3$. Since $

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one-one but not onto

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(B) To determine if $f(x) = x^3$ is one-one and onto for $f: N ightarrow N$:$1$. One-one check: Let $f(x_1) = f(x_2)$. Then $x_1^3 = x_2^3$. Since $x_1, x_2 \in N$,this implies $x_1 = x_2$. Thus,the function is one-one.$2$. Onto check: For a function to be onto,the range must equal the codomain $(N)$. For $x = 2 \in N$,$f(2) = 2^3 = 8$. However,for an element like $y = 2 \in N$ (codomain),there is no $x \in N$ such that $x^3 = 2$ (since $\sqrt[3]{2} 
otin N$). Thus,the function is not onto.Therefore,the function is one-one but not onto.

$f: N \rightarrow N, f(x) = x^3$ is . . . . . . .

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