The domain of the function
f(x) = log7{ log3(log5(20x – x2 – 91 ))} is:
Explanation:
f(x) = log7{ log3(log5(20x – x2 – 91 ))}
As log of negative numbers is not defined,
log3 (log5 (20x - x2 - 91)) > 0
∴ log5 (20x - x2 - 91)) > 30
∴ log5 (20x - x2 - 91) > 1
∴ 20x - x2 - 91 > 5
∴ 20x - x2 - 96 > 0
∴ x2 - 20x + 96 < 0
∴ (x - 12) (x - 8) < 0
∴ 8 < x < 12
Hence, option (b).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.