https://file.aiquickdraw.com/mathbot/file/1726621888122lyy6o3do.jpg

The problem asks for \( f(g(x)) \), where:

- \( f(x) = 6x - 3 \)
- \( g(x) = 5x + 4 \)

To solve \( f(g(x)) \), we need to substitute \( g(x) \) into \( f(x) \).

Let's calculate step by step:

1. Start with \( g(x) = 5x + 4 \).
2. Now substitute \( g(x) \) into \( f(x) \):
   \[
   f(g(x)) = f(5x + 4) = 6(5x + 4) - 3
   \]
3. Expand and simplify:
   \[
   f(5x + 4) = 6 \cdot 5x + 6 \cdot 4 - 3 = 30x + 24 - 3 = 30x + 21
   \]

Thus, \( f(g(x)) = 30x + 21 \).

The correct answer is \( \boxed{c} \).

Let me know if you want further details or have any questions! Here are some related questions for practice:

1. What is the general formula for the composition of two functions?
2. How do you find the inverse of a function?
3. If \( h(x) = f(g(x)) \), how would you differentiate \( h(x) \)?
4. How does the order of composition affect the result, i.e., is \( f(g(x)) \) the same as \( g(f(x)) \)?
5. What happens to \( f(g(x)) \) if \( g(x) \) is a constant function?

**Tip:** Always expand terms carefully when substituting functions to avoid algebraic errors.

Diketahui f(x)=6x-3, g(x)=5x+4 sehingga (fog)(x)=___

Learn how to solve the function composition problem involving f(x) = 6x - 3 and g(x) = 5x + 4. Step-by-step explanation on how to calculate f(g(x)) and simplify the expression. Suitable for Grades 8-10.

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