Let's break down the problem step by step: ### Given - \( F^{10}_0 f(x) = 7 \) ### Find - \( F^{10}_0 - 3 f(x) \) #### Step 1: Understand the notation - \( F^{10}_0 f(x) \) likely means some operation (possibly a transformation, summation, or functional operator) applied to \( f(x) \), resulting in \( 7 \). - The question asks for \( F^{10}_0 - 3 f(x) \), which means we subtract \( 3f(x) \) from \( F^{10}_0 f(x) \). #### Step 2: Substitute the known value Since \( F^{10}_0 f(x) = 7 \): \[ F^{10}_0 f(x) - 3f(x) = 7 - 3f(x) \] #### Step 3: Final Answer \[ \boxed{7 - 3f(x)} \] **Explanation:** You take the given value of the functional operation (\( 7 \)) and subtract \( 3f(x) \) as instructed. The answer depends on the value of \( f(x) \), but in terms of \( f(x) \), the result is \( 7 - 3f(x) \).