Solveeit Logo
Login

Question

Question: Domain of f(x) is [-1, 2] then domain of f([x] − x<sup>2</sup> + 4) where [.] denotes the greatest i...

Domain of f(x) is [-1, 2] then domain of f([x] − x2 + 4) where [.] denotes the greatest integer function, is

A

[−1,7][ - 1 , \sqrt { 7 } ]

B

[−3,−1]∪[3,7][ - \sqrt { 3 } , - 1 ] \cup [ \sqrt { 3 } , \sqrt { 7 } ]

C

(−1,7]( - 1 , \sqrt { 7 } ]

D

[−3,−1)∪[3,7)[ - \sqrt { 3 } , - 1 ) \cup [ \sqrt { 3 } , \sqrt { 7 } )

Answer

[−3,−1]∪[3,7][ - \sqrt { 3 } , - 1 ] \cup [ \sqrt { 3 } , \sqrt { 7 } ]

Explanation

Solution

We must have -1 ≤ [x] − x2 + 4 ≤ 2

⇒ x2 – 5 ≤ [x] ≤ x2 – 2

If x2 – 5 = ± 2 ⇒ x = −3,7- \sqrt { 3 } , \sqrt { 7 }

If x2 - 2 = ±1 ⇒ x = 3\sqrt { 3 }

⇒ Required values of x are

[−3,−1]∪[3,7][ - \sqrt { 3 } , - 1 ] \cup [ \sqrt { 3 } , \sqrt { 7 } ]