1. The problem asks: If $f$ is a decreasing function, what is the direction (increasing or decreasing) of the function $g = f \circ f$, which means $g(x) = f(f(x))$. 2. Recall that a function $f$ is decreasing if for any $x_1 < x_2$, we have $f(x_1) > f(x_2)$. 3. To analyze $g(x) = f(f(x))$, consider two points $x_1 < x_2$. 4. Since $f$ is decreasing, $f(x_1) > f(x_2)$. 5. Now apply $f$ again to these values: $g(x_1) = f(f(x_1))$ and $g(x_2) = f(f(x_2))$. 6. Because $f$ is decreasing, applying it to $f(x_1)$ and $f(x_2)$ reverses the inequality: since $f(x_1) > f(x_2)$, then $f(f(x_1)) < f(f(x_2))$. 7. Therefore, for $x_1 < x_2$, $g(x_1) < g(x_2)$, which means $g$ is increasing. Final answer: If $f$ is decreasing, then $g = f \circ f$ is increasing.