Sets, Relations & Functions
Domain of sec⁻¹ of Rational Function
nta_pyq_2023_apr
Grade 11
Question:
If the domain of $f(x)=\sec^{-1}\!\left(\dfrac{2x}{5x+3}\right)$ is $[\alpha,\beta)\cup(\gamma,\delta]$, then $|3\alpha+10(\beta+\gamma)+21\delta|$ is equal to __________
Step-by-Step Solution
Key Concept: $\sec^{-1}$ domain requires $\left|\frac{2x}{5x+3}\right|\geq1$. Solve $\frac{2x}{5x+3}\leq-1$ or $\frac{2x}{5x+3}\geq1$.
Domain $=[-1,-\frac{3}{5})\cup(-\frac{3}{5},-\frac{3}{7}]$. $|\cdot|=24$.
Correct Answer: 24