Sets, Relations & Functions
Functions
nta_pyq_2025_jan
Grade 11
Question:
If the domain of the function log (18x - x - 77) is (\alpha, \beta) and the domain of the function log 5 2 (x-1) ( 2x +3x-2 2 ) is x -3x-4 (\gamma, \delta) , then \alpha + \beta + \gamma is equal to : 2 2 2
Step-by-Step Solution
Key Concept: Apply the core result for domains, ranges and functional equations and simplify using the given constraints.
2 f1 (x) = log (18x - x - 77) 5 (3) \therefore 18x - x 2 - 77 > 0 2 x - 18x + 77 < 0 x \in (7, 11) \alpha = 7, \beta = 11 2 2x + 3x - 2 f2 (x) = log ( ) (x-1) 2 x - 3x - 4 2 2x + 3x - 2 x > 1, x - 1 \ne 1, > 0 2 x - 3x - 4 (2x - 1)(x + 2) x > 1, x \ne 2, > 0 (x - 4)(x + 1) \therefore x \in (4, \infty) \therefore \gamma = 4 2 2 2 \therefore \alpha + \beta + \gamma = 49 + 121 + 16 = 186
Correct Answer: 3