JEE Mains · Maths · STD 12 - 1. relation and function
Let the domain of the function\(f(x)=\log _3 \log _5\left(7-\log _2\left(x^2-10 x+85\right)\right)+\sin ^{-1}\left(\left|\frac{3 x-7}{17-x}\right|\right)\)be \((\alpha, \beta]\). Then \(\alpha+\beta\) is equal to :
- A 10
- B 12
- C 9
- D 8
Answer & Solution
Correct Answer
(C) 9
Step-by-step Solution
Detailed explanation
Let \(x ^2-10 x +85=\lambda\) ∴ Domain for first term \(\lambda>0\)\(\quad\)....(1) \(\&\ 7-\log _2 \lambda>0 \Rightarrow \lambda<2^7\)\(\quad\)....(2) \(\& \log _5\left(7-\log _2 \lambda\right)>0 \Rightarrow \lambda<2^6\)\(\quad\)....(3) ∴ from (1), (2) & (3) \(0<\lambda<2^6\)…
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