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To solve \( f(g(16)) \), given the functions:

\[
f(x) = x^3 - 7x, \quad g(x) = \sqrt{4x}
\]

### Step-by-step solution:

1. **Evaluate \( g(16) \)**:
   \[
   g(16) = \sqrt{4 \times 16} = \sqrt{64} = 8
   \]

2. **Now calculate \( f(g(16)) = f(8) \)**:
   \[
   f(8) = 8^3 - 7 \times 8
   \]
   First, calculate \( 8^3 \) and \( 7 \times 8 \):
   \[
   8^3 = 512, \quad 7 \times 8 = 56
   \]
   Now subtract:
   \[
   f(8) = 512 - 56 = 456
   \]

Thus, \( f(g(16)) = 456 \).

Would you like any further details or have additional questions?

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Here are 5 related questions to expand your understanding:

1. What happens if you substitute \( x = 25 \) into \( f(g(x)) \)?
2. Can you explain why \( g(x) = \sqrt{4x} \) simplifies to \( g(16) = 8 \)?
3. How would the result change if the function \( f(x) \) was different, say \( f(x) = x^2 + 2x \)?
4. Could \( f(g(x)) \) ever be negative? Why or why not?
5. What is the domain and range of the composite function \( f(g(x)) \)?

**Tip**: Always evaluate inner functions first when working with composite functions!

Given the functions f(x) = x^3 - 7x and g(x) = sqrt(4x), evaluate the function f(g(x)) for x = 16. Give your answer in exact form.

Learn how to evaluate the composite function f(g(x)) for x = 16, given f(x) = x^3 - 7x and g(x) = sqrt(4x). This step-by-step solution covers composite function operations, cube functions, and square roots. Suitable for students in Grades 9-12.

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