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CGP EDU Academic Team
Published on: August 11, 2026
Find the domain of the function f(x) = log {log |sinx| {x 2 –8x +23) – 
}
Text Solution
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Sol. For f(x) to be defined; log |sinx| (x 2 –8x + 23)
– 
> 0
⇒ log |sinx| (x 2 –8x + 23) – 3 log |sinx| 2 > 0
⇒ log |sinx| 
> 0
⇒ 
< |sinx| 0 ; As |sinx| ≠ 0, 1 and
0 < |sinx| < 1.
⇒ x 2 –8x + 23 < 8
⇒ x 2 –8x + 15 < 0 and sin x ≠ 0, ± 1
(x –3) (x –5) < 0 and x ≠ n π , (2n +1) π /2
⇒ x ∈ (3, 5) and x ≠ π , 
∴ domain is x ∈ (3, π ) ∪ 
∪ 
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