1. The problem asks us to determine the correct relationship between the function $f(x)$ and the tangent line $g(x)$ to the curve $y=f(x)$ at any point $(x,y)$. 2. Recall that the tangent line to a curve at a point touches the curve exactly at that point and has the same slope as the curve there. 3. The equation of the tangent line at $x$ is given by: $$g(x) = f(a) + f'(a)(x - a)$$ where $a$ is the point of tangency. 4. Since the tangent line approximates the curve near $a$, the value of $g(x)$ is generally close to $f(x)$ near $a$. 5. For a curve that is concave up (like the one described, becoming steeper), the tangent line lies below the curve except at the point of tangency. 6. This means: $$g(x) \leq f(x)$$ for values of $x$ near $a$, with equality only at $x=a$. 7. Therefore, the correct statement is (b) $g(x) \leq f(x)$. Final answer: (b) $g(x) \leq f(x)$