If h(x) is the inverse of f(x), what is the value of h(f(x))?

If \( h(x) \) is the inverse of \( f(x) \), then the relationship between the functions \( h(x) \) and \( f(x) \) can be described using the properties of inverse functions.

By definition of inverse functions:

\[
f(h(x)) = x \quad \text{and} \quad h(f(x)) = x
\]

These equations hold true because applying a function and then its inverse (or vice versa) returns the original input.

Given this, the value of \( h(f(x)) \) is simply:

\[
h(f(x)) = x
\]

### Summary
Since \( h(x) \) is the inverse of \( f(x) \), \( h(f(x)) = x \). This means applying \( f(x) \) followed by its inverse \( h(x) \) will return the original input \( x \).

Would you like to know more about inverse functions, or do you have any other questions?

### Related Questions:
1. What is the definition of an inverse function?
2. How do you find the inverse of a function algebraically?
3. What are some examples of functions and their inverses?
4. How does the graph of a function relate to the graph of its inverse?
5. Can all functions have inverses?

**Tip:** To find the inverse of a function algebraically, swap the roles of \( x \) and \( y \) and solve for \( y \).

Explore the relationship between functions h(x) and f(x) when h(x) is the inverse of f(x). Learn the definition of inverse functions and how they interact algebraically. Suitable for high school students and anyone interested in understanding inverse functions.

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