Trigonometry & Inverse Trigonometry
Inverse Trigonometric Functions
Grade 12
Question:
<p>Find the number of solutions to the equation <p>\(y = |x^2 - 1| = |\tan^{-1}|x||\)</p>
Step-by-Step Solution
Key Concept: Graphical method to find intersections of two curves: plot both functions and count intersection points.
<p><strong>Solution:</strong> From the graph of $y = |x^2 - 1|$ and $y = |\tan^{-1}|x||$, we can see that these two curves intersect at exactly 4 points.</p><p>∴ The equation has <strong>4 solutions</strong>.</p>
Correct Answer: 4