The function f: R rightarrow R is defined by | vedclass

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

Question

(C) Given the function $f: R \rightarrow R$ defined by $f(x) = 3^{-x}$.$I$. For one-one check: Let $f(x_1) = f(x_2)$.$3^{-x_1} = 3^{-x_2} \Rightarrow

Vedclass · Accepted Answer

Only $I, III$

Vedclass · Answer

(C) Given the function $f: R ightarrow R$ defined by $f(x) = 3^{-x}$.$I$. For one-one check: Let $f(x_1) = f(x_2)$.$3^{-x_1} = 3^{-x_2} \Rightarrow -x_1 = -x_2 \Rightarrow x_1 = x_2$.Since $f(x_1) = f(x_2) \Rightarrow x_1 = x_2$,the function is one-one.$II$. For onto check: The range of $f(x) = 3^{-x}$ is $(0, \infty)$,which is a subset of the codomain $R$. Since the range $
eq$ codomain,the function is not onto.$III$. For decreasing check: $f'(x) = \frac{d}{dx}(3^{-x}) = -3^{-x} \ln 3$. Since $3^{-x} > 0$ and $\ln 3 > 0$,$f'(x) Therefore,statements $I$ and $III$ are true.

The function $f: R \rightarrow R$ is defined by $f(x)=3^{-x}$. Observe the following statements about it:
$I$. $f$ is one-one
$II$. $f$ is onto
$III$. $f$ is a decreasing function
Which of these statements are true?

Similar Questions

$A$ photoelectric cell is illuminated by a point source of light $1\;m$ away. When the source is shifted to $2\;m$,then:

The solution set of $(5+4 \cos \theta)(2 \cos \theta+1)=0$ in the interval $[0, 2 \pi]$ is:

The density of water at $20^oC$ is $0.998 \ g/cm^3$ and at $40^oC$ is $0.992 \ g/cm^3$. The mean coefficient of cubical expansion (in per ${}^oC$) is

The force between the plates of a parallel plate capacitor of capacitance $C$ and distance of separation of the plates $d$ with a potential difference $V$ between the plates,is

For all integers $n \geq 1$, which of the following is divisible by $9$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

The function $f: R \rightarrow R$ is defined by $f(x)=3^{-x}$. Observe the following statements about it:$I$. $f$ is one-one$II$. $f$ is onto$III$. $f$ is a decreasing functionWhich of these statements are true?