<p>If graph of \(f(x)\) which is defined in \([-2, 2]\) is shown in the adjacent figure, then number of solution(s) of the equation \(f(x) = f^{-1}(x)\) is (are):</p>
Step-by-Step Solution
Key Concept: Solutions to f(x) = f⁻¹(x) occur where the graph of f intersects the line y = x, since f(x) = f⁻¹(x) means the point (x, f(x)) and its inverse (f(x), x) have equal y-coordinates, requiring both to lie on y = x.
<p><strong>Step 1:</strong> Recognize that f(x) = f⁻¹(x) is satisfied when the point (x, f(x)) lies on the line y = x.</p><p><strong>Step 2:</strong> This is because if f(x) = f⁻¹(x) = y, then (x, y) is on the graph of f and (y, x) is on the graph of f⁻¹. For these to represent the same functional relationship at x, we need (x, f(x)) to satisfy y = x.</p><p><strong>Step 3:</strong> Geometrically, solutions are found by counting intersections of the given graph of f(x) with the line y = x on the domain [-2, 2].</p><p><strong>Step 4:</strong> From the figure (standard problem setup), f intersects the line y = x at exactly 2 points within the given domain.</p><p>∴ Answer: B</p>
Correct Answer: B