1. The problem asks about the shape of the inverse function $g(x) = f^{-1}(x)$ given that $f(x)$ is increasing and convex upward. 2. Recall that if $f$ is increasing, then its inverse $f^{-1}$ is also increasing. 3. For convexity, if $f$ is convex upward (concave up), then its inverse $f^{-1}$ is convex downward (concave down). 4. This is because the curvature of the inverse function reverses the convexity of the original function. 5. Therefore, since $f$ is increasing and convex upward, $g = f^{-1}$ is increasing and convex downward. 6. The correct answer is (b) increasing and convex downward.