Math Problem Statement
If two functions f and g are inverses, then
(fcircle◦g)(x)equals=
Solution
If two functions and are inverses, then the composition of and , denoted as , equals .
In other words:
This is a key property of inverse functions: applying one function followed by its inverse returns the original input.
Would you like further details or have any questions?
Here are 5 related questions to consider:
- What is the definition of an inverse function?
- How do you determine if two functions are inverses algebraically?
- What is the graphical interpretation of inverse functions?
- Can every function have an inverse?
- How do you find the inverse of a function?
Tip: To verify if two functions are inverses, check both and .
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Math Problem Analysis
Mathematical Concepts
Inverse Functions
Function Composition
Algebra
Formulas
(f ∘ g)(x) = f(g(x)) = x
(g ∘ f)(x) = g(f(x)) = x
Theorems
Inverse Function Property
Suitable Grade Level
Grades 10-12
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