Math Problem Statement
(F°g) (×) =f(g) (×) =f(ײ-9)
Solution
The equation in the image appears to represent the composition of two functions and the evaluation of one of them at a specific point. Let's break it down:
The notation means the composition of functions and , and it is defined as:
In the image, the equation proceeds as follows:
This suggests that the function is defined as:
Thus, the composition of and , evaluated at , is given by substituting into :
Do you need help with a specific part of this problem, or would you like further details on function composition or solving this kind of expression?
Here are five related questions that can extend your understanding:
- How do you find the composition of two arbitrary functions and ?
- If and , what is ?
- What are the conditions for two functions to be composed?
- How can the domain of be affected by the domain of ?
- How does the composition of functions differ from multiplication of functions?
Tip: Always check the domain of both functions when composing them, as the domain of the composition is restricted by the domain of the inner function.
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Math Problem Analysis
Mathematical Concepts
Function Composition
Algebra
Formulas
(f ° g)(x) = f(g(x))
g(x) = x² - 9
Theorems
Function Composition Rule
Suitable Grade Level
Grades 10-12
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