Math Problem Statement
Express the function in the form
f ∘ g.
(Use non-identity functions for f and g.)
G(x) =
cube root (x/2+x)
Solution
We are given the function , and we want to express it in the form , which means we are looking for two functions and such that .
Step-by-step decomposition:
-
Inner function : This will represent the expression inside the cube root.
-
Outer function : This will apply the cube root operation to the result of .
Thus, we can express as:
So the functions and are:
Would you like further details or clarifications on this? Here are some related questions to explore:
- How do we identify the inner and outer functions for composition?
- What are the general properties of composition of functions?
- How does the cube root affect the domain of the function?
- How can we verify if the decomposition is correct?
- Can we generalize this method to other root functions?
Tip: When composing functions, start by identifying the most complex operation (usually the outer function) and then work inward.
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Math Problem Analysis
Mathematical Concepts
Function Composition
Cube Root
Algebraic Manipulation
Formulas
G(x) = f(g(x))
g(x) = x/2 + x = 3x/2
f(x) = cube root(x)
Theorems
Function Composition
Suitable Grade Level
Grades 10-12
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