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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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_

Vedclass · Accepted Answer

One-one but not onto

Vedclass · Answer

(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

Similar Questions

Let $A = \{0, 1, 2, 3, 4, 5, 6, 7\}$. Then the number of bijective functions $f: A \rightarrow A$ such that $f(1) + f(2) = 3 - f(3)$ is equal to $.....$

The number of bijective functions $f : \{1, 3, 5, 7, \ldots, 99\} \rightarrow \{2, 4, 6, 8, \ldots, 100\}$ such that $f(3) \geq f(9) \geq f(15) \geq f(21) \geq \ldots \geq f(99)$ is:

The function defined by $f(x) = \frac{2x+3}{3x+4}, x \neq -\frac{4}{3}$ is

$f: X \rightarrow R$,where $X = \{x \mid 0 < x < 1\}$,is defined as $f(x) = \frac{2x-1}{1-|2x-1|}$. Then:

If $R$ denotes the set of all real numbers,then the function $f: R \to R$ defined by $f(x) = [x]$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module