Operating on Functions ~adapted from Walch Education

Arithmetic Operations on Functions Combine linear and exponential expressions using addition: (f + g)(x) = f(x) + g(x). In other words, add the two functions together by combining like terms. Combine linear and exponential expressions using subtraction: (f – g)(x) = f(x) – g(x). In other words, subtract the second function from the first while making sure to distribute the negative across all terms of the second function.

Arithmetic Operations on Functions, continued Combine linear and exponential expressions using multiplication: (f • g)(x) = f(x) • g(x). In other words, multiply the two functions together. Combine linear and exponential expressions using division: (f ÷ g)(x) = f(x) ÷ g(x). In other words, divide the first function by the second function. Use a fraction bar to display the final function.

Practice If f(x) = 3x + 2 and g(x) = 2x – 7, what is the result of adding the two functions? In other words, what is (f + g)(x)? How do you represent this algebraically?

The Solution Add the two function rules. Simplify the equation. (f + g)(x) = f(x) + g(x) (f + g)(x) = (3x + 2) + (2x – 7) Simplify the equation. (f + g)(x) = 3x + 2x + 2 – 7 (f + g)(x) = 5x – 5

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