f: N rightarrow N,is defined by f(x)=x^6 then | vedclass

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(C) Given $f: N \rightarrow N$ defined by $f(x) = x^6$.$1$. Check for one-one:Let $f(x_1) = f(x_2)$ for $x_1, x_2 \in N$.$x_1^6 = x_2^6$.Since $x_1, x

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$f$ is one-one but not onto

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(C) Given $f: N \rightarrow N$ defined by $f(x) = x^6$.$1$. Check for one-one:Let $f(x_1) = f(x_2)$ for $x_1, x_2 \in N$.$x_1^6 = x_2^6$.Since $x_1, x_2 \in N$ (natural numbers are positive),we have $x_1 = x_2$.Thus,$f$ is one-one.$2$. Check for onto:$A$ function is onto if the range equals the codomain $(N)$.For $f(x) = x^6$,the range is ${1^6, 2^6, 3^6, \dots} = {1, 64, 729, \dots}$.Since the range is not equal to the codomain $N$ (e.g.,$2 \in N$ but there is no $x \in N$ such that $x^6 = 2$),$f$ is not onto.Therefore,$f$ is one-one but not onto.

$f: N \rightarrow N$,is defined by $f(x)=x^6$ then, . . . . . . .

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