Functions
Domain via log and inverse trig; counting integers
Grade Class 12
Question:
Find the number of integers in the domain of $f(x)=\dfrac{1}{\sqrt{\ln\cos^{-1}x}}$.
Step-by-Step Solution
Key Concept: $\cos^{-1}x$ defined for $x\in[-1,1]$. Need $\ln(\cos^{-1}x)>0\Leftrightarrow\cos^{-1}x>1\Leftrightarrow x<\cos1\approx0.54$. Integer $x$: $\{-1,0\}$.
2 integers ($x=-1$ and $x=0$).
Correct Answer: 2