Sets, Relations & Functions
Domain of Composite Log and Inverse Trig Function
nta_pyq_2023_apr
Grade 11
Question:
If the domain of $\log_e\!\left(\dfrac{6x^2+5x+1}{2x-1}\right)+\cos^{-1}\!\left(\dfrac{2x^2-3x+4}{3x-5}\right)$ is $(\alpha,\beta)\cup(\gamma,\delta)$, then $18(\alpha^2+\beta^2+\gamma^2+\delta^2)$ is equal to
Step-by-Step Solution
Key Concept: For $\ln$: $\frac{6x^2+5x+1}{2x-1}>0$. For $\cos^{-1}$: $-1\leq\frac{2x^2-3x+4}{3x-5}\leq1$. Intersect all conditions.
$18(\alpha^2+\beta^2+\gamma^2+\delta^2)=20$.
Correct Answer: 20