1. The problem states that the curve is given by $y = f(x)$ and the tangent line at any point $(x, y)$ on the curve is given by $y = g(x)$. 2. By definition, the tangent line $g(x)$ at a point on the curve $f(x)$ touches the curve exactly at that point and has the same slope as the curve at that point. 3. Since the tangent line just touches the curve and does not cross it at the point of tangency, the value of $g(x)$ at that point equals $f(x)$. 4. However, for points near the tangent point, the tangent line can lie above or below the curve depending on the concavity of $f(x)$. 5. Given the curve resembles $y = \sqrt{x}$, which is concave down for $x > 0$, the tangent line lies above the curve near the point of tangency. 6. Therefore, for all $x$ near the point of tangency, $g(x) \geq f(x)$. 7. Among the options: - (a) $g(x) = f(x)$ only at the tangent point, not generally. - (b) $g(x) \leq f(x)$ is false for this curve. - (c) $g(x) \geq f(x)$ is true near the tangent point. - (d) $f(x) + g(x) < 0$ is not generally true since both are positive. Final answer: (c) $g(x) \geq f(x)$