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2.4 operations on functions

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This document discusses evaluating expressions involving functions using addition, subtraction, multiplication, division, and composition. It provides examples of defining functions f(x) and g(x) and evaluating expressions like f(3) - g(-1) and 2f(1). Tables are given showing the evaluation of functions like f(x), g(x) and others based on their definitions. Composition is described as taking the output of one function as the input of another, written as f(g(x)).

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2.4 operations on functions
We can evaluate expressions that involve adding, subtracting, multiplying, and dividing the output values of functions.  Example:  Let f(x) = 2x + 1 and g(x) = -3x – 5  Evaluate:  f(3) – g(-1)  2f(1)
 Use these function definitions to evaluate the expressions below: g f (1)  f (3) x f(x) 1 -2 2 -4 x 3 -8 4 0 g(2)  g(5) g(5) 3 f (1)
 Use these function definitions to evaluate: g(x) 1. 2. 3. 4. k(2)  k(2) k (  2)  k (0) 3
 A fifth operation (along with +, -, ×, ÷) is called composition.  Composition takes a function, and uses it as the input for another function.  Can be written: f(g(x))
 Use the function definitions to evaluate: m(x)  3 2x t v(t) 2 -4 4 0 6 7 8 3 10 1
 Use the function definitions to evaluate: 푝 푡 = −푡 + 2

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2.4 operations on functions

  • 2. We can evaluate expressions that involve adding, subtracting, multiplying, and dividing the output values of functions.  Example:  Let f(x) = 2x + 1 and g(x) = -3x – 5  Evaluate:  f(3) – g(-1)  2f(1)
  • 3.  Use these function definitions to evaluate the expressions below: g f (1)  f (3) x f(x) 1 -2 2 -4 x 3 -8 4 0 g(2)  g(5) g(5) 3 f (1)
  • 4.  Use these function definitions to evaluate: g(x) 1. 2. 3. 4. k(2)  k(2) k (  2)  k (0) 3
  • 5.  A fifth operation (along with +, -, ×, ÷) is called composition.  Composition takes a function, and uses it as the input for another function.  Can be written: f(g(x))
  • 6.  Use the function definitions to evaluate: m(x)  3 2x t v(t) 2 -4 4 0 6 7 8 3 10 1
  • 7.  Use the function definitions to evaluate: 푝 푡 = −푡 + 2