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Question: Domain of f(x) = \(\sqrt{2\{ x\}^{2} - 3\{ x\} + 1}\)where {.} denotes the fractional part, in [-1, ...

Domain of f(x) = 2{x}2−3{x}+1\sqrt{2\{ x\}^{2} - 3\{ x\} + 1}where {.} denotes the fractional part, in [-1, 1], is

A

[−1,1]∼(12,1)[ - 1,1 ] \sim \left( \frac { 1 } { 2 } , 1 \right)

B

[−1,−12]∪[0,12]∪{1}\left[ - 1 , - \frac { 1 } { 2 } \right] \cup \left[ 0 , \frac { 1 } { 2 } \right] \cup \{ 1 \}

C

[−1,12]\left[ - 1 , \frac { 1 } { 2 } \right]

D

[−12,1]\left[ - \frac { 1 } { 2 } , 1 \right]

Answer

[−1,−12]∪[0,12]∪{1}\left[ - 1 , - \frac { 1 } { 2 } \right] \cup \left[ 0 , \frac { 1 } { 2 } \right] \cup \{ 1 \}

Explanation

Solution

We must have

2{x}2 − 3{x} + 1 ≥ 0 ⇒ {x} ≥ 1 or {x} ≤ 1/2

Thus we have 0 <{x} ≤ 1/2

⇒ x ∈ [n,n+12]\left[ n , n + \frac { 1 } { 2 } \right] , n ∈ I.