To find \( f(x + h) \) for the given function \( f(x) = 2x - 1 \), we simply substitute \( x + h \) in place of \( x \) in the original function:

\[
f(x + h) = 2(x + h) - 1
\]

Now simplify:

\[
f(x + h) = 2x + 2h - 1
\]

Thus, \( f(x + h) = 2x + 2h - 1 \).

Would you like further details or have any questions?

Here are some related questions:

1. How do you find \( f(2x) \) for the same function \( f(x) = 2x - 1 \)?
2. What is the difference between \( f(x+h) \) and \( f(x) \)?
3. How does \( f(x+h) \) relate to the concept of a derivative?
4. How can you calculate \( f(h) \) in this case?
5. What happens when you substitute a negative value for \( h \) in \( f(x+h) \)?

**Tip:** Understanding how to manipulate function arguments (like \( x + h \)) is crucial for grasping the fundamentals of calculus and algebraic transformations.

Learn how to calculate f(x + h) for the linear function f(x) = 2x - 1. This problem involves function substitution, simplifying expressions, and key algebraic concepts. Suitable for students in Grades 9-11.

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