Task 6:

Let f(x)=2x^2-4x and g(x)=x-3.

	Determine f(g(4)).

To determine \( f(g(4)) \), we need to follow these steps:

1. **Find \( g(4) \)**:
   \[
   g(x) = x - 3
   \]
   Substituting \( x = 4 \):
   \[
   g(4) = 4 - 3 = 1
   \]

2. **Substitute \( g(4) \) into \( f(x) \)**:
   \[
   f(x) = 2x^2 - 4x
   \]
   Substitute \( x = 1 \) (since \( g(4) = 1 \)):
   \[
   f(1) = 2(1)^2 - 4(1)
   \]
   Simplifying:
   \[
   f(1) = 2(1) - 4 = 2 - 4 = -2
   \]

So, \( f(g(4)) = -2 \).

Would you like more details or have any questions? Here are some related problems to consider:

1. Determine \( g(f(4)) \) given the same functions \( f(x) \) and \( g(x) \).
2. Evaluate \( f(g(x)) \) as a function of \( x \) instead of a specific value.
3. Find the inverse functions of \( f(x) \) and \( g(x) \), if they exist.
4. Determine the value of \( f(g(-2)) \).
5. Solve for \( x \) if \( f(g(x)) = 0 \).

**Tip:** Always evaluate inner functions first when dealing with composite functions.

Learn how to evaluate f(g(4)) using composite functions f(x) = 2x^2 - 4x and g(x) = x - 3. Follow step-by-step calculations to find the value of f(g(4)), a common problem in high school algebra.

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