14. If f(x) = 3x + 6 and g(x) = 𝑥3 + 3 then g[f(x)]=
A) (5-x) B) (x-5) C)(x+3) D) (x+5)
15. If f(x) = 4x – 1 and g(x) = 𝑥4 + 14 then f[g(x)]=
A) (3-x) B) (x-3) C) x D) (x-1)
اختر بس

Let's solve each function composition one at a time.

### 14. For \( g[f(x)] \)

1. **Find \( f(x) \)**:
   \[
   f(x) = 3x + 6
   \]

2. **Substitute \( f(x) \) into \( g(x) \)**:
   \[
   g[f(x)] = g(3x + 6) = (3x + 6)^3 + 3
   \]
   This expression is complex, but we can analyze the answer choices instead.

   - After substitution and simplification, you can check values for \( x \) to find which answer matches.

   Evaluating the original functions with a specific \( x \) (e.g., \( x = 0 \)):
   \[
   f(0) = 6 \implies g(6) = 6^3 + 3 = 216 + 3 = 219
   \]

   None of the options fit directly, but checking specific values or further simplifying might help find the right form.

### 15. For \( f[g(x)] \)

1. **Find \( g(x) \)**:
   \[
   g(x) = x^4 + 14
   \]

2. **Substitute \( g(x) \) into \( f(x) \)**:
   \[
   f[g(x)] = f(x^4 + 14) = 4(x^4 + 14) - 1 = 4x^4 + 56 - 1 = 4x^4 + 55
   \]
   Again, check values for \( x \) to find which matches.

### Answers
1. For the first function \( g[f(x)] \), further simplification or substitution is required to find an exact match.
2. For the second function \( f[g(x)] \), it simplifies to \( 4x^4 + 55 \), which doesn’t match given options.

It seems neither question has a straightforward answer from the provided options without further evaluation. 

Would you like further details on these calculations or help with any specific part? Here are some related questions:

1. How do you evaluate a function at a specific point?
2. What is the process of function composition?
3. Can you explain how to simplify polynomial expressions?
4. What techniques are used to analyze complex function compositions?
5. How do you approach finding roots of polynomial functions?

**Tip:** When dealing with compositions, substituting specific values can sometimes clarify the function's behavior without needing full simplification.

14. If f(x) = 3x + 6 and g(x) = x^3 + 3 then g[f(x)]= A) (5-x) B) (x-5) C) (x+3) D) (x+5) 15. If f(x) = 4x – 1 and g(x) = x^4 + 14 then f[g(x)]= A) (3-x) B) (x-3) C) x D) (x-1)

Explore the function composition problems involving f(x) = 3x + 6 and g(x) = x^3 + 3, as well as f(x) = 4x - 1 and g(x) = x^4 + 14. This page provides a detailed solution and analysis of the results for each composition.

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