Math Problem Statement

If two functions f and g are​ inverses, then

​(fcircle◦​g)(x)equals=

Solution

If two functions ff and gg are inverses, then the composition of ff and gg, denoted as (fg)(x)(f \circ g)(x), equals xx.

In other words: (fg)(x)=f(g(x))=x(f \circ g)(x) = f(g(x)) = x

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:

  1. What is the definition of an inverse function?
  2. How do you determine if two functions are inverses algebraically?
  3. What is the graphical interpretation of inverse functions?
  4. Can every function have an inverse?
  5. How do you find the inverse of a function?

Tip: To verify if two functions are inverses, check both (fg)(x)=x(f \circ g)(x) = x and (gf)(x)=x(g \circ f)(x) = x.

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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