<p>The graph of the function \(y = f(x)\) is symmetrical about the line \(x = 2\), then</p>
Step-by-Step Solution
Key Concept: If a function's graph is symmetric about the vertical line x = 2, then f(2 + t) = f(2 - t) for all t in the domain. This means the function satisfies f(x) = f(4 - x), which is the functional equation for symmetry about x = 2.
<p><strong>Step 1:</strong> Understand that if the graph of y = f(x) is symmetric about the vertical line x = 2, then the function is equidistant from this line on both sides.</p><p><strong>Step 2:</strong> Let a point (2 + t, y) be on the graph. By symmetry, the point (2 - t, y) must also be on the graph for any value of t.</p><p><strong>Step 3:</strong> This means f(2 + t) = f(2 - t) for all t in the domain.</p><p><strong>Step 4:</strong> Substituting x = 2 + t (so t = x - 2), we get: f(x) = f(2 - (x - 2)) = f(4 - x)</p><p><strong>Step 5:</strong> Therefore, the function satisfies the condition <strong>f(x) = f(4 - x)</strong>, which is the defining property when a function is symmetric about x = 2.</p><p>∴ Answer: B</p>
Correct Answer: B