Operations with Functions

If you have two functions, you can conduct operations such as adding, subtracting, multiplying, and dividing with the functions. Look over the following list of operations:

1. Sum: (f + g)(x) = f(x) + g(x)
2. Difference: (f – g)(x) = f(x) – g(x)
3. Product: (f • g)(x) = f(x) • g(x)
4. Quotient:

Let’s take a look at an example. Let f(x) = 2x + 6 and g(x) = 4x – 9.

1. Find the sum of f(x) and g(x).
   
   f(x) + g(x) = 2x + 6 + (4x – 9)                                                                                     
   f(x) + g(x) = 6x – 3
    
2. Find the difference of f(x) and g(x).
   
   f(x) – g(x) = 2x + 6 – (4x – 9)
   
   Remember to distribute the negative. This is a common mistake that you want to avoid.
   f(x) – g(x) = 2x + 6 – 4x + 9
   
   f(x) – g(x) = –2x + 15
    
3. Find the product of f(x) and g(x).
   
   f(x) • g(x) = (2x + 6)(4x – 9)
   
   Use the FOIL Method.
   f(x) • g(x) = 8x² – 18x + 24x – 54
   
   Combine like terms
   f(x) • g(x) = 8x² + 6x – 54
    
4. Find the quotient of f(x) and g(x).