Let the domain of the function f ( x ) = log 3 log 5 ( 7 - log 2 ( x 2 - 10 x + 85 ) ) + sin - 1 ( | 3 x - 7 17 - x | ) be . T h e n is equal to: [2026]

Question

Let the domain of the function $f (x) = \log_{3} \log_{5} (7 - \log_{2} (x^{2} - 10 x + 85)) + \sin^{- 1} (| \frac{3 x - 7}{17 - x} |)$ be $(α, β] . Then α + β$ is equal to: [2026]

Smart Achievers · Accepted Answer

(3)

$Let x^{2} - 10 x + 85 = λ$

$∴$ $Domain for first term$

$λ > 0 . . . (1)$

$& 7 - \log_{2} λ > 0 \Rightarrow λ < 2^{7} . . . (2)$

$& \log_{5} (7 - \log_{2} λ) > 0 \Rightarrow λ < 2^{6} . . . (3)$

$∴$ $from (1), (2) & (3)$

$0 < λ < 2^{6}$

$0 < x^{2} - 10 x + 85 < 64$

$\Rightarrow x \in (3, 7) . . . (A)$

$& domain for second term - 1 \leq \frac{3 x - 7}{x - 17} \leq 1$

$\Rightarrow x \in [- 5, 6] . . . (B)$

$From (A) & (B), domain of function will be (3, 6]$

$\Rightarrow α = 3, β = 6$

$\Rightarrow α + β = 9$

Solution

Q.
Let the domain of the function $f (x) = \log_{3} \log_{5} (7 - \log_{2} (x^{2} - 10 x + 85)) + \sin^{- 1} (| \frac{3 x - 7}{17 - x} |)$ be $(α, β] . Then α + β$ is equal to: [2026]

1 8

2 10

3 9

4 12

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Solution

Q. Let the domain of the function f(x)=log3log5 (7-log2(x2-10x+85))+sin-1 (|3x-717-x|) be (α,β]. Then α+β is equal to: [2026]

1 8

2 10

3 9

4 12

Want Us to Email you About Special Offers & Updates?

Q.
Let the domain of the function $f (x) = \log_{3} \log_{5} (7 - \log_{2} (x^{2} - 10 x + 85)) + \sin^{- 1} (| \frac{3 x - 7}{17 - x} |)$ be $(α, β] . Then α + β$ is equal to: [2026]