Given the function \( f(x) = \frac{4}{x} \), you are looking to evaluate the function at \( x = a + h \).

Substituting \( x = a + h \) into the function \( f(x) \), we get:

\[
f(a+h) = \frac{4}{a+h}
\]

This is the expression for \( f(a+h) \) when \( f(x) = \frac{4}{x} \).

Would you like further details on how this relates to other concepts, such as the difference quotient?

Here are five related questions:

1. How would you compute the difference quotient \(\frac{f(a+h) - f(a)}{h}\) for this function?
2. What does the expression \( f(a+h) \) represent in the context of a function's rate of change?
3. How does the limit of \(\frac{f(a+h) - f(a)}{h}\) as \( h \) approaches 0 relate to the derivative of \( f(x) \)?
4. How would you interpret \( f(a+h) \) geometrically on the graph of \( f(x) \)?
5. What is the significance of evaluating a function at \( a + h \) in calculus?

**Tip**: Understanding the difference quotient is crucial, as it is the foundation for finding the derivative, which represents the rate of change of a function.

Explore how to evaluate the function f(x) = 4/x at x = a + h. This page covers the definition of f(a+h), its relation to the difference quotient, and its significance in calculus. Suitable for advanced high school students and anyone interested in calculus concepts.

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