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Understanding Operations with Functions

Learn how to perform operations such as sum, difference, quotient, and product on functions, including finding values and determining domains. Explore composition of functions and inverse functions with helpful examples and methods. Check your understanding with practice questions.

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Understanding Operations with Functions

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  1. Section 1.1.3 Operations with Functions

  2. Operations with Functions Let f and g be any two functions. • We define as follows:

  3. Operations with Functions Let f and g be any two functions. Domain: f__________ g ___________ Finding the value : _________________________________ Find

  4. Operations with Functions Let f and g be any two functions. • We define as follows: Sum: _________________________________ Domain: ___________________________ Find ( f + g ) (x) and determine the domain

  5. Operations with Functions Let f and g be any two functions. Difference: _________________________________ Domain: ___________________________ Find ( f - g ) (x) and determine the domain

  6. Operations with Functions Let f and g be any two functions. • Quotient: _________________________________ Domain: ___________________________ Find and determine the domain

  7. Operations with Functions Let f and g be any two functions. • Product: _______________________ written _____ or _____ Domain: ___________________________ Find (fg)(x) and determine the domain Careful: ____________________________________________________________

  8. Composition of Functions: _________________________________________ • Forms: ________________________________________ ________________________________________

  9. Inverse of a Function Inverse of a Function ____________________________________________________ Notation : ____________________________ read ___________________________________ ( Caution: __________________________________________ )

  10. Defn: (words) ____________________________________________________ If _______________________________________ then ____________________________________ Defn: (math) ____________________________________________________ ____________________________________________________

  11. Method to find an inverse: ____________________________________________________ ____________________________________________________ Check : Find f(4)

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