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The problem shown in the image asks you to compute the composition of functions \( (fg)(0) \), where \( f(x) = x^2 - 17 \) and \( g(x) = 6 - x \).

We want to find \( (fg)(0) \), which means we need to apply the function \( f \) to \( g(0) \).

Let's break this down:

1. **Find \( g(0) \)**: 
   \[
   g(0) = 6 - 0 = 6
   \]

2. **Substitute \( g(0) = 6 \) into \( f(x) \)**:
   \[
   f(g(0)) = f(6)
   \]
   Now calculate \( f(6) \):
   \[
   f(6) = 6^2 - 17 = 36 - 17 = 19
   \]

Thus, \( (fg)(0) = 19 \).

Would you like further details or explanations on this?

Here are some related questions to expand understanding:
1. What is the general rule for function composition?
2. How would the result change if \( f(x) \) and \( g(x) \) were different?
3. How can you determine if two functions are inverses of each other?
4. What is the domain of the composed function \( (fg)(x) \)?
5. How does function composition differ from function multiplication?

**Tip**: When performing function composition, always apply the inner function first, then substitute the result into the outer function.

Let f(x) = x^2 - 17 and g(x) = 6 - x. Perform the composition or operation indicated: (fg)(0).

Learn how to find the composition of functions f(x) = x^2 - 17 and g(x) = 6 - x. The detailed solution involves substituting values to find (fg)(0). This problem covers key concepts in function composition, quadratic functions, and substitution, suitable for Grades 10-12.

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