Let the domains of the functions f ( x ) = lo g 4 lo g 3 lo g 7 ( 8 − lo g 2 ( x 2 + 4 x + 5 ) ) and g ( x ) = sin − 1 ( x − 2 7 x + 10 ) be ( α , β ) and [ γ , δ ] , respectively. Then α 2

Question

Let the domains of the functions f ( x ) = lo g 4 ​ lo g 3 ​ lo g 7 ​ ( 8 − lo g 2 ​ ( x 2 + 4 x + 5 ) ) and g ( x ) = sin − 1 ( x − 2 7 x + 10 ​ ) be ( α , β ) and [ γ , δ ] , respectively. Then α 2 + β 2 + γ 2 + δ 2 is equal to :-

TestHub · Accepted Answer

​ lo g 3 ​ ( lo g 7 ​ ( 8 − lo g 2 ​ ( x 2 + 4 x + 5 ) ) ) > 0 lo g 2 ​ ( x 2 + 4 x + 5 ) < 1 x 2 + 4 x + 3 < 0 ⇒ x ∈ ( − 3 , − 1 ) − 1 ≤ x − 2 7 x + 10 ​ ≤ 1 ⇒ x ∈ [ − 2 , − 1 ] α = − 3 , β = − 1 , γ = − 2 , δ = − 1 α 2 + β 2 + γ 2 + δ 2 = 15 option ( 1 ) ​

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