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

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(D) The function $f:R 	o R$ is defined by $f(x) = e^x$. To check for one-one: Let $x_1, x_2 \in R$ such that $f(x_1) = f(x_2)$. Then $e^{x_1} = e^{x_

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One-one but not onto

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(D) The function $f:R 	o R$ is defined by $f(x) = e^x$. To check for one-one: Let $x_1, x_2 \in R$ such that $f(x_1) = f(x_2)$. Then $e^{x_1} = e^{x_2}$,which implies $x_1 = x_2$. Thus,the function is one-one. To check for onto: The range of $f(x) = e^x$ is $(0, \infty)$,which is a subset of the codomain $R$. Since the range is not equal to the codomain (e.g.,negative values and zero have no pre-image),the function is not onto. Therefore,the function is one-one but not onto.

The function $f:R \to R$ defined by $f(x) = e^x$ is

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