Function Composition Calculator

How to Use the Function Composition Calculator

Welcome to the Function Composition Calculator! This tool is designed to help you explore the composition of mathematical functions f(x) and g(x). Follow the steps below to learn how to use this tool effectively:

Step 1: Select Function f(x)

• Locate the field labeled Select Function f(x).
• Click on the dropdown menu to reveal the list of available functions.
• Choose a function based on the expression you want to use for f(x). The choices include:
  • f(x) = 2x
  • f(x) = x²
  • f(x) = √x
  • f(x) = sin(x)
  • f(x) = cos(x)

Step 2: Select Function g(x)

• Locate the field labeled Select Function g(x).
• Click on the dropdown menu to reveal the list of available functions, similar to Step 1.
• Select the desired function for g(x) from the available options. Ensure it complements the function chosen for f(x).

Step 3: Input Value x

• Find the field labeled Input value x.
• Type a numerical value in the range of -100 to 100 into the input box.
• You may use decimal increments, but they must be in steps of 0.1.

Step 4: View Results

• Once you have selected the functions and input your value of x, the calculator will automatically compute the results.
• You will see values for the following results rounded to four decimal places:
  • f(x): This shows the output of function f with your chosen x value.
  • g(x): This indicates the output of function g using the same x value.
  • f∘g(x) = f(g(x)): This displays the result of the composition where g(x) is applied first, followed by f.
  • g∘f(x) = g(f(x)): This shows the outcome when f(x) is evaluated first and then passed to g.

By following these steps, you can efficiently use the Function Composition Calculator to study the effects of combining different functions. Feel free to experiment with various combinations to understand better how function composition operates!