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3.5 Operations on Functions

3.5 Operations on Functions - Operations on Operations...

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Unformatted text preview: Operations on Operations Functions Functions Section 3.5 Sum, Difference, Product, and Quotient of Functions Quotient ( f + g )( x) = f ( x) + g ( x) ( f − g )( x) = f ( x) − g ( x) ( fg )( x) = f ( x) • g ( x) f f ( x) ÷( x) = g ( x) g Composite Functions Composite If f and g are functions, then the composite function of f and g is ( g o f )( x) = g ( f ( x)) The expression is read “g circle f ” or “f followed by g.” Note the order carefully; the functions are applied right to left. Domains of Composite Functions Domains Let f and g be functions. The domain of g o f is the set of all real numbers x such that x is in the domain of f f(x) is in the domain of g Joke Time Joke What do you call a line of rabbits walking backwards? a receding “hare” line Why did Dracula’s mom give Why did Dracula’s mom give him cough syrup? because he was coffin ...
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