Function Operations - The Basics
Just like numbers, functions can be added, subtracted, multiplied, and divided. Each operation creates a new function by combining the original functions in different ways.
Here are the key operations: f+g(x) = f(x) + g(x) for addition, f−g(x) = f(x) - g(x) for subtraction, (f·g)(x) = f(x) · g(x) for multiplication, and f/g(x) = f(x)/g(x) for division (where g(x) ≠ 0).
Function composition (f∘g)(x) = f(g(x)) is special - you're putting one function inside another. Think of it as a two-step process where you first evaluate the inner function, then use that result in the outer function.
Quick Check: For division, always identify where the denominator equals zero - these x-values are excluded from the domain!