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Adding and Subtracting Functions

Adding and Subtracting Functions

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Adding and Subtracting Functions

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Tutorial

  • Adding Two Functions
  • Subtracting Two Functions

Adding Two Functions

Suppose we were given two functions f(x) and g(x) and asked to add them together. Because both of these functions are given in terms of the variable x (remember that f(x) means "x is an argument of the function f") we can combine the functions together by adding the like terms in each. For example, suppose f left parenthesis x right parenthesis equals 2 x squared minus x plus 5 and g left parenthesis x right parenthesis space equals space x squared minus 5 x plus 1. If we wanted to find f(x) + g(x) we simply do the following:

When trying to add two functions defined by the same variable often times you will see the notation (f + g)(x), which just means f(x) + g(x).

Sometimes we may be asked to evaluate two functions for different values first and then add the result. For instance, suppose f(x) = 2x - 1 and g(x) = 3x and we are asked to find the result of f(2) + g(1). In cases like this, we first need to evaluate each function of the given value and then add the final results, as shown below:

Subtracting Two Functions

 

When subtracting two functions we follow the same rules outlined above for addition only this time we have a negative sign between the two functions. For example, if we had the functions f left parenthesis x right parenthesis space equals space x space minus space 1 and g left parenthesis x right parenthesis space equals space x cubed minus 2 x plus 1 and asked to find f(x) - g(x) we would need to do the following:

Always remember to distribute the negative when subtracting functions, otherwise your calculation will be incorrect.

Now if were were asked to find f(3) - g(3) for the functions f left parenthesis x right parenthesis space equals space x minus 1 and g left parenthesis x right parenthesis equals x cubed minus 2 x plus 1we can use the same method we did above since both functions are being evaluated for the same value of x and both are in terms of x. Once we get to the last step in the above example we simply need to substitute in 3 for x and solve evaluate.

When trying to subtract two functions defined by the same variable often times you will see the notation (f - g)(x), which just means f(x) - g(x).

Keep in mind that if f(x) are defined using different variables or for different value and you are asked to find f(x) - g(x) you first need to evaluate each function for the given value of its variable and then subtract the final results.