Sets, Relations & Functions
Domain of Combined Log and Inverse Trig
nta_pyq_2023_apr
Grade 11
Question:
If the domain of $f(x)=\ln_e(4x^2+11x+6)+\sin^{-1}(4x+3)+\cos^{-1}\!\left(\dfrac{10x+6}{3}\right)$ is $(\alpha,\beta]$, then $36|\alpha+\beta|$ is equal to
Step-by-Step Solution
Key Concept: Intersect: $\ln$ needs $4x^2+11x+6>0$; $\sin^{-1}$ needs $-1\leq4x+3\leq1$; $\cos^{-1}$ needs $-1\leq\frac{10x+6}{3}\leq1$.
Domain $[-\frac{3}{4},-\frac{1}{2}]$. $36|\alpha+\beta|=45$.
Correct Answer: 4