If two functions f and g are​ inverses, then 

​(fcircle◦​g)(x)equals=

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

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

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 \( (f \circ g)(x) = x \) and \( (g \circ f)(x) = x \).

If two functions f and g are inverses, then (f ∘ g)(x) equals = ?

Learn how inverse functions work and the key property of their composition. This problem demonstrates how the composition of two inverse functions f and g results in the identity function, returning the original input. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation