Math Problem Statement
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Solution
We are given two functions:
We need to find the value of , which represents the composition of and evaluated at .
Step 1: Find
First, we substitute into the function :
Step 2: Find
Now that we know , we substitute this value into the function :
Thus, the value of is .
The correct answer is:
Would you like further explanation or have any other questions?
Related Questions:
- What is the domain of the composite function ?
- If , how would the composite function change?
- What happens if ? Why is it excluded?
- Can we always compose two functions, or are there restrictions?
- How can the composition of functions be applied to real-world problems?
Tip:
When evaluating composite functions, always work from the inside out, starting with the innermost function.
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Math Problem Analysis
Mathematical Concepts
Function Composition
Algebra
Formulas
f(x) = 3x - 5
g(x) = (4x - 2) / (6 - 4x)
Function composition: (g o f)(x) = g(f(x))
Theorems
-
Suitable Grade Level
Grades 10-12
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