If the domain of the function f ( x ) = lo g 7 ( 1 − lo g 4 ( x 2 − 9 x + 18 ) ) is ( α , β ) ∪ ( γ , δ ) , then α + β + γ + δ is equal to

Question

If the domain of the function f ( x ) = lo g 7 ​ ( 1 − lo g 4 ​ ( x 2 − 9 x + 18 ) ) is ( α , β ) ∪ ( γ , δ ) , then α + β + γ + δ is equal to

TestHub · Accepted Answer

Domain 1 − lo g 4 ( x 2 − 9 x + 18 ) > 0 Also x 2 − 9 x + 18 > 0 ( x − 3 ) ( x − 6 ) > 0 x ∈ ( − ∞ , 3 ) ∪ ( 6 , ∞ ) ...(1) also x 2 − 9 x + 18 < 4 x 2 − 9 x + 14 < 0 x ∈ ( 2 , 7 ) ...(2) ( 1 ) ∩ ( 2 ) ( 2 , 3 ) ∪ ( 6 , 7 ) = ( α , β ) ∪ ( γ , δ ) ⇒ α + β + γ + δ = 18

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