JEE Mains · Maths · STD 11- 2. Relation and Function
If the domain of the function \(\log _5\left(18 x-x^2-77\right)\) is \((\alpha, \beta)\) and the domain of the function \(\log _{(x-1)}\left(\frac{2 x^2+3 x-2}{x^2-3 x-4}\right)\) is \((\gamma, \delta)\), then \(\alpha^2+\beta^2+\gamma^2\) is equal to :
- A 195
- B 179
- C 186
- D 174
Answer & Solution
Correct Answer
(C) 186
Step-by-step Solution
Detailed explanation
\begin{aligned} & f_1(x)=\log _5\left(18 x-x^2-77\right) \\ & \therefore 18 x-x^2-77>0 \\ & \quad x^2-18 x+77 < 0 \\ & x \in(7,11) \\ & \alpha=7, \beta=11 \\ & f_2(x)=\log _{(x-1)}\left(\frac{2 x^2+3 x-2}{x^2-3 x-4}\right) \\ & x>1, x-1 \neq 1, \frac{2 x^2+3 x-2}{x^2-3 x-4}>0 \\…
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