♦Perform arithmetic ope rations on functions
♦Perform composition of functions
Definitions
If f(x) and g(x) both exist, the sum , difference , product ,
quotient and composition of two functions f and g are defined by
•Addition 

•Subtraction 

•Multiplication 

•Division 

•Composition 

Examples of Evaluating Combinations of Functions –Using
Symbolic Representations
Let f(x) = x^2 + 2xand g(x) = 3x1
Find the symbolic re presentation for the function f + g
and use this to evaluate (f + g)(2)
or Evaluate each function, then combine
Let f(x) = x^2 + 2xand g(x) = 3x−1
Find the symbolic representation for the function fg and
use this to evaluate (fg)(2)
Or
Example of Composition of Functions:
Let f(x) = x^2 + 2xand g(x) = 3x1
Find the symbolic representation for the function
and use this to evaluate ()(2)
Example of Composition of Functions:
Let f(x) = x^2 + 2xand g(x) = 3x1
Find the symbolic representation for the function
and use this to evaluate ()(2)
Example:
Let f(x) = 15x and
Find
Find
Example: Composition from tabular displays for
functions.
Find ()(1)
Find
Find
Evaluating Combinations of
Functions Numerically
•Given numerical representations for f and and g in the
table
•Evaluate combinations of f and and g as specified.
Examples:
Answers: