Find the Domain of sec-1x − tan-1x
Solution:
Given function:
\[ f(x) = \sec^{-1}(x) – \tan^{-1}(x) \]
Step 1: Domain of sec⁻¹(x)
\[ x \leq -1 \quad \text{or} \quad x \geq 1 \]
Step 2: Domain of tan⁻¹(x)
\[ x \in \mathbb{R} \]
Step 3: Intersection
\[ (-\infty, -1] \cup [1, \infty) \]
Final Answer:
Domain = \[ (-\infty, -1] \cup [1, \infty) \]