Domain of function f(x) = log|5{x} - 2x| is x | vedclass

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

Question

(B) The function $f(x) = \log|5\{x\} - 2x|$ is defined when $5\{x\} - 2x 
eq 0$.We need to find the values of $x$ for which $5\{x\} - 2x = 0$.Since $

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(B) The function $f(x) = \log|5\{x\} - 2x|$ is defined when $5\{x\} - 2x 
eq 0$.We need to find the values of $x$ for which $5\{x\} - 2x = 0$.Since $x = [x] + \{x\}$,we have $\{x\} = x - [x]$.Substituting this into the equation: $5(x - [x]) - 2x = 0$.$5x - 5[x] - 2x = 0 \Rightarrow 3x = 5[x] \Rightarrow [x] = \frac{3x}{5}$.Since $[x]$ is an integer,$\frac{3x}{5}$ must be an integer. Let $\frac{3x}{5} = k$,where $k \in Z$. Then $x = \frac{5k}{3}$.Also,we know that $k \le x Substituting $x = \frac{5k}{3}$: $k \le \frac{5k}{3} $3k \le 5k From $3k \le 5k$,we get $2k \ge 0 \Rightarrow k \ge 0$.From $5k Since $k$ is an integer,$k$ can be $0$ or $1$.If $k = 0$,$x = \frac{5(0)}{3} = 0$.If $k = 1$,$x = \frac{5(1)}{3} = \frac{5}{3}$.Thus,the set $A = \{0, \frac{5}{3}\}$.The number of elements $n(A) = 2$.

Function	Range
$A. f(x) = \|x\|$	$I. [0, \infty)$
$B. f(x) = x^2$	$II. \mathbb{R}$
$C. f(x) = x^3$	$III. [0, \infty)$
$D. f(x) = \text{sgn}(x)$	$IV. \{-1, 0, 1\}$

Domain of function $f(x) = \log|5\{x\} - 2x|$ is $x \in R - A$,then $n(A)$ is (where $\{.\}$ denotes fractional part function)

Similar Questions

Match the following functions with their respective ranges:
Function Range
$A. f(x) = |x|$ $I. [0, \infty)$
$B. f(x) = x^2$ $II. \mathbb{R}$
$C. f(x) = x^3$ $III. [0, \infty)$
$D. f(x) = \text{sgn}(x)$ $IV. \{-1, 0, 1\}$

The range of the function $f(x) = \frac{x^2+x+1}{x^2-x+1}$ is

Range of the function $f(x) = \frac{x^2 + x + 2}{x^2 + x + 1}; x \in R$ is

If $[x]$ represents the greatest integer function, then the set of all real values of $x$ for which $f(x)=\sqrt{\frac{[x]-x}{x-[x]}}$ is real is

The range of the real valued function $f(x) = \frac{x^2 + 2x - 15}{2x^2 + 13x + 15}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module