If denotes the fractional part of x, the range of the function f(x) = √ x 2-2 x is

Question

If denotes the fractional part of x, the range of the function f(x) = √ x 2-2 x is (A) φ (B) [0, 1/2] (C) 0, 1/2 (D) 0

Tardigrade Admin · Accepted Answer

x2 -2 x ge 0 ⇒ x x -2 ge 0 ⇒ x le 0 or x ge 2 Second case is not possible. Hence x = 0, as x le [0, 1). Hence range of f (x) contains only one element 0.

Q. If { } denotes the fractional part of x, the range of the function $f (x) = {x}^{2} - 2 {x}$ is

$ϕ$

$[0, 1/2]$

$0, 1/2$

$0$

${x^{2}} - 2 {x} \geq 0$
$\Rightarrow {x} {x} - 2 \geq 0$
$\Rightarrow {x} \leq 0$ or ${x} \geq 2$
Second case is not possible.
Hence ${x} = 0$ , as ${x} \leq [0, 1)$ . Hence range of $f (x)$ contains only one element $0.$

Q. If { } denotes the fractional part of x, the range of the function f(x)={x}2−2{x}​ is

ϕ

[0,1/2]

0,1/2

0

{x2}−2{x}≥0 ⇒{x}{x}−2≥0 ⇒{x}≤0 or {x}≥2 Second case is not possible. Hence {x}=0, as {x}≤[0,1). Hence range of f(x) contains only one element 0.

Q. If { } denotes the fractional part of x, the range of the function $f (x) = {x}^{2} - 2 {x}$ is

$ϕ$

$[0, 1/2]$

$0, 1/2$

$0$

${x^{2}} - 2 {x} \geq 0$
$\Rightarrow {x} {x} - 2 \geq 0$
$\Rightarrow {x} \leq 0$ or ${x} \geq 2$
Second case is not possible.
Hence ${x} = 0$ , as ${x} \leq [0, 1)$ . Hence range of $f (x)$ contains only one element $0.$