Sets, Relations & Functions
Domain of Combined Function
nta_pyq_2024_apr
Grade 11
Question:
If the domain of the function $\sin^{-1}\left(\dfrac{3x-22}{2x-19}\right)+\log_e\left(\dfrac{3x^2-8x+5}{x^2-3x-10}\right)$ is $(\alpha,\beta]$, then $3\alpha+10\beta$ is equal to:
Step-by-Step Solution
Key Concept: For $\sin^{-1}$: $-1\leq\frac{3x-22}{2x-19}\leq1$. For $\log$: $\frac{3x^2-8x+5}{x^2-3x-10}>0$. Intersect both conditions.
Domain $(5,41/5]$. $3\alpha+10\beta=15+82=97$.
Correct Answer: 3