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Adding and Subtracting Functions

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- 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 and . 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 and 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 and we 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.