Math Problem Statement
Solution
The image contains a problem regarding composition of functions. It states the following:
Given:
The task is to find .
To solve this:
- Start with .
- Now, substitute into . This means replacing in with .
Thus:
So, the complete expression is:
Would you like further clarification on this? Here are 5 related questions for further practice:
- What is the composition of for the same functions and ?
- If and , what is ?
- How do you find the inverse of a function, and what is the inverse of ?
- What are the domain and range of the composed function ?
- How do we differentiate the composite function ?
Tip: When composing functions, always substitute the entire function inside the variable of the other function, treating it as a replacement for the variable.
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Math Problem Analysis
Mathematical Concepts
Function Composition
Algebra
Formulas
g(f(x)) = g(f(x)) = x^2 - 1
Theorems
Function Composition Theorem
Suitable Grade Level
Grades 9-10
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