Math Problem Statement

If f(x) = 2x + 1, what would the function look like once you substitute in a 1 to find f(1)?

Solution

The question asks to evaluate the function f(x)=2x+1f(x) = 2x + 1 by substituting x=1x = 1 to find f(1)f(1).

Let's go through it step-by-step:

  1. Start with the function: f(x)=2x+1f(x) = 2x + 1

  2. Substitute x=1x = 1 to find f(1)f(1): f(1)=2(1)+1f(1) = 2(1) + 1

  3. Calculate the expression: f(1)=2+1=3f(1) = 2 + 1 = 3

The correct choice that matches this setup is:

  • f(1) = 2(1) + 1

This is the middle (green) option on the screen.

Would you like a further breakdown or have additional questions on this?


Here are five related questions to deepen understanding:

  1. What would the function look like if you substituted x=2x = 2 instead?
  2. How do you interpret the value of f(1)=3f(1) = 3 in a real-world context if this function represents a scenario?
  3. What would be the result if the function were f(x)=3x+2f(x) = 3x + 2 and you substituted x=1x = 1?
  4. How do you determine if a function is linear, like f(x)=2x+1f(x) = 2x + 1?
  5. How would the function change if the constant were increased to 2, making it f(x)=2x+2f(x) = 2x + 2?

Tip: When substituting values into a function, carefully replace only the variable, and keep the rest of the function's structure the same.

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Math Problem Analysis

Mathematical Concepts

Algebra
Function Evaluation

Formulas

f(x) = 2x + 1

Theorems

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Suitable Grade Level

Grades 6-8