Let Let f(x) = log4(1 – log7(x^2 – 9x + 8)). If the domain of f(x) is (α, β) ∪ (γ, δ). Then α + β + γ + δ equal to

Question

Let \(f(x)=\log _{4}\left(1-\log _{7}\left(x^{2}-9 x+8\right)\right).\) If the domain of f(x) is \((\alpha, \beta) \cup(\gamma, \delta).\) Then \(\alpha+\beta+\gamma+\delta\) equals to

(1) 18

(2) 27

(3) 21

(4) 9

Answer 1

Correct option is: (1) 18 

\(1-\log _{7}\left(x^{2}-9 x+8\right)>0\)

\(\Rightarrow \log _{7}\left(x^{2}-9 x+8\right)<1\)

\(\Rightarrow x^{2}-9 x+8<7\)

\(\Rightarrow x^{2}-9 x+1<0\)