Math Problem Statement
- 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)
- 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
Solution
Let's solve each function composition one at a time.
14. For
-
Find :
-
Substitute into : This expression is complex, but we can analyze the answer choices instead.
- After substitution and simplification, you can check values for to find which answer matches.
Evaluating the original functions with a specific (e.g., ):
None of the options fit directly, but checking specific values or further simplifying might help find the right form.
15. For
-
Find :
-
Substitute into : Again, check values for to find which matches.
Answers
- For the first function , further simplification or substitution is required to find an exact match.
- For the second function , it simplifies to , 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:
- How do you evaluate a function at a specific point?
- What is the process of function composition?
- Can you explain how to simplify polynomial expressions?
- What techniques are used to analyze complex function compositions?
- 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.
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Math Problem Analysis
Mathematical Concepts
Function Composition
Polynomial Functions
Formulas
f(x) = 3x + 6
g(x) = x^3 + 3
f(x) = 4x - 1
g(x) = x^4 + 14
Theorems
Composition of Functions
Suitable Grade Level
Grades 9-11
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