The function f: R to R defined by f(x) = x^2 | vedclass

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(D) function $f: R 	o R$ is an injection (one-one) if $f(x_1) = f(x_2) \implies x_1 = x_2$. For $f(x) = x^2$,we have $f(1) = 1^2 = 1$ and $f(-1) = (-

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Neither injection nor surjection

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(D) function $f: R 	o R$ is an injection (one-one) if $f(x_1) = f(x_2) \implies x_1 = x_2$. For $f(x) = x^2$,we have $f(1) = 1^2 = 1$ and $f(-1) = (-1)^2 = 1$. Since $f(1) = f(-1)$ but $1 
eq -1$,the function is not an injection. $A$ function $f: R 	o R$ is a surjection (onto) if for every $y \in R$,there exists an $x \in R$ such that $f(x) = y$. For $f(x) = x^2$,the range is $[0, \infty)$,which is a subset of the codomain $R$. Since there are negative values in the codomain that have no pre-image in the domain (e.g.,$y = -1$),the function is not a surjection. Therefore,the function is neither an injection nor a surjection.

The function $f: R \to R$ defined by $f(x) = x^2$ for all $x \in R$ is

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