EDGE Math 8

Operations on Functions

Operations such as addition, subtraction, multiplication, and division can also be performed on functions. Function composition can also be evaluated given two functions.

Given two functions f and g:

1. The sum of f and g, denoted by $f + g,$ is the function defined by

(f + g) (x) = f (x) + g (x) .

2. The difference of f and g, denoted by $f - g,$ is the function defined by

(f - g) (x) = f (x) - g (x) .

3. The product of f and g, denoted by $f \cdot g,$ is the function defined by

(f \cdot g) (x) = f (x) \cdot g (x) .

4. The quotient of f and g, denoted by $\frac{f}{g},$ is the function defined by

(\frac{f}{g}) (x) = \frac{f (x)}{g (x)},

provided that

g (x) \neq 0.

5. The composite function of f and g, denoted by $f \circ g,$ is the function defined by

(f \circ g) (x) = f (g (x)) .

Similarly, the composite function of g and f, denoted by $g \circ f,$ is the function defined by

(g \circ f) (x) = g (f (x)) .