Math Problem Statement

f(x) = x-5 y g(x) = x*2 - 1

Solution

You provided two functions:

  1. f(x)=x5f(x) = x - 5
  2. g(x)=2x1g(x) = 2x - 1

What would you like to do with these functions? You could:

  • Find values for f(x)f(x) and g(x)g(x) at specific xx values.
  • Compose the functions (e.g., f(g(x))f(g(x)) or g(f(x))g(f(x))).
  • Find the inverse functions.
  • Solve for xx when f(x)=g(x)f(x) = g(x).

Please specify your goal.


Here are 5 questions to extend this:

  1. What is the value of f(3)f(3) and g(3)g(3)?
  2. How would you compute f(g(x))f(g(x))?
  3. What is the graph of f(x)f(x) and g(x)g(x)?
  4. Can f(x)f(x) and g(x)g(x) intersect? If so, where?
  5. What happens when you solve f(x)=0f(x) = 0 and g(x)=0g(x) = 0?

Tip: Function composition is a useful tool when combining different processes into a single step.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions
Function Composition

Formulas

f(x) = x - 5
g(x) = 2x - 1
f(g(x)) = f(2x - 1) = (2x - 1) - 5 = 2x - 6
g(f(x)) = g(x - 5) = 2(x - 5) - 1 = 2x - 10 - 1 = 2x - 11

Theorems

Linear function behavior
Function composition

Suitable Grade Level

Grades 8-10