Math Problem Statement

Given f(x) = 2x - 1 find f(x + h)

Solution

To find f(x+h)f(x + h) for the given function f(x)=2x1f(x) = 2x - 1, we simply substitute x+hx + h in place of xx in the original function:

f(x+h)=2(x+h)1f(x + h) = 2(x + h) - 1

Now simplify:

f(x+h)=2x+2h1f(x + h) = 2x + 2h - 1

Thus, f(x+h)=2x+2h1f(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)f(2x) for the same function f(x)=2x1f(x) = 2x - 1?
  2. What is the difference between f(x+h)f(x+h) and f(x)f(x)?
  3. How does f(x+h)f(x+h) relate to the concept of a derivative?
  4. How can you calculate f(h)f(h) in this case?
  5. What happens when you substitute a negative value for hh in f(x+h)f(x+h)?

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

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Function Substitution

Formulas

f(x) = 2x - 1
f(x + h) = 2(x + h) - 1

Theorems

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Suitable Grade Level

Grades 9-11