Functions
Domains of nested logarithms
nta_pyq_2025_apr
Grade 12
Question:
Let the domains of the functions and$g(x) = sin$be ($\alpha$,$\beta$) and [$\gamma$,$\delta$], respectively.$Then -1$$7x+10$2 f$(x) = log$log log$(8 - log$$(x + 4x + 5))$( ) 4 3 7 2$x-2$$\alpha$2 +$\beta$2 +$\gamma$2 +$\delta$2 is equal to :-
Step-by-Step Solution
Key Concept: Impose every domain restriction from logarithms, roots, denominators, and inverse functions before intersecting intervals.
log (log$(8 - log$$(x + 4x + 5))) > 0$3 7 2 2 (1) 2 log$(x + 4x + 5) < 1$2 2$x + 4x + 3 < 0$$\Rightarrow$ x$\ in $$(-3$, -1)$7x + 10 - 1$$\le$$\le$1$x - 2$$\Rightarrow$ x$\ in $[-2, -1]$\alpha$= -3,$\beta$= -1,$\gamma$= -2,$\delta$= -1 2 2 2 2$\alpha$+$\beta$+$\gamma$+$\delta$= 15 option (1)
Correct Answer: 1