Function f: R rightarrow R defined by f(x) = | vedclass

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(A) To determine if $f(x) = x^3$ is one-one and onto: $1$. For one-one: Let $f(x_1) = f(x_2)$,then $x_1^3 = x_2^3$. Taking the cube root on both sides

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one-one and onto

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(A) To determine if $f(x) = x^3$ is one-one and onto: $1$. For one-one: Let $f(x_1) = f(x_2)$,then $x_1^3 = x_2^3$. Taking the cube root on both sides,we get $x_1 = x_2$. Since $f(x_1) = f(x_2) \implies x_1 = x_2$,the function is one-one. $2$. For onto: For any $y \in R$ (codomain),we need to find $x \in R$ (domain) such that $f(x) = y$. Since $x^3 = y$,we have $x = y^{1/3}$. Since $y^{1/3}$ is defined for all real numbers $y$,for every $y \in R$,there exists an $x = y^{1/3} \in R$. Thus,the function is onto. Therefore,$f$ is one-one and onto.

Function $f: R \rightarrow R$ defined by $f(x) = x^3$ is . . . . . . .

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