Sets, Relations & Functions
Domain of Combined Function — $6(\alpha+\beta+\gamma+\delta)$
nta_pyq_2026_jan
Grade 11
Question:
If the domain of the function $f(x)=\sin^{-1}\!\left(\dfrac{5-x}{2x+3}\right)+\dfrac{1}{\log_e(10-x)}$ is $(-\infty,\alpha]\cup[\beta,\gamma)-\{\delta\}$, then $6(\alpha+\beta+\gamma+\delta)$ is equal to
Step-by-Step Solution
Key Concept: For $\sin^{-1}$: $-1\leq\tfrac{5-x}{2x+3}\leq1$ and $2x+3\neq0$. For $\log$: $10-x>0$ and $10-x\neq1$. Combine all conditions.
$\alpha=-8$, $\beta=\tfrac{2}{3}$, $\gamma=10$, $\delta=9$. $6(\alpha+\beta+\gamma+\delta)=70$.
Correct Answer: 3