# UB MTH 309 - 2.6_Combinations of Functions (28 pages)

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## 2.6_Combinations of Functions

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- Pages:
- 28
- School:
- University at Buffalo, The State University of New York
- Course:
- Mth 309 - Intro Linear Algebra

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Section 2 6 Combinations of Functions Composite Functions The Domain of a Function 3x 5 x2 4x 5 x 2 4 x 5 0 g x x 5 x 1 0 x 5 0 x 1 0 x 5 x 1 Domain 1 1 5 5 h x 2 x 5 2 x 5 0 2x 5 5 x 2 5 Domain 2 Domains of Other Functions f x 4 x 5 Domain f x x 2 7 x Domain f x 3 x Domain Example Find the domain of the function 4x 1 f x 3x 2 Example Find the domain of the function f x 4x 1 The Algebra of Functions f can be g simplified determine the domain If the function before simplifying Example f x x 2 4 and g x x 2 f f x 2 in Domain of g g 2 2 f x 2 4 x 2 x 2 x 2 x g x 2 x 2 Determining Domains When Adding or Subtracting Functions The domain of f g is the set of all real numbers that are common to the domain of f and the domain of g Thus we must find the domains of f and g before finding their intersection Suppose f x x 3 and g x x 2 then f g x x 3 x 2 Now for their domains f x x 3 x 3 0 g x x 2 x 2 0 x 3 x 2 So the domain for the sum of the functions is x 2 which in interval notation is 2 Continued on next slide The graph of f g x x 3 x 2 confirms that the domain of this function is 2 y x Continuation of the same problem Determining Domains when Multiplying Functions The domain of f g is the set of all real numbers that are common to the domain of f and the domain of g y Thus we must find the domains of f and g before finding their intersection 5 3 Suppose f x and g x then x x 2 15 fg x x x 2 Now for their domains 5 3 f x g x x x 2 x 0 x 2 0 x 2 So the domain for the product of the functions is x 0 x 2 which in interval notation is 0 0 2 2 Example If f x 5x 1 g x x 2 2 x 1 Find each of the following f g x f g x fg x f x g Example If f x 5x 1 g x 5x 2 9 x 2 Find the domain of the following fg x f x g Example 1 1 If f x g x Find the domain x 2x 1 of the following fg x f x g Example If f x x 1 g x x 6 Find the domain for f g x Composite Functions f g

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