Functions-Lec5-classnotes.pdf - Combination of functions \u2022 Addition\/subtraction:f \u00b1 g(x = f(x \u00b1 g(x Ex 1 Let f(x = tan(x and g(x = of f g cos(x x2

Functions-Lec5-classnotes.pdf - Combination of functions...

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Combination of functions Addition/subtraction: f ± g ( x ) = f ( x ) ± g ( x ) Ex. 1. Let f ( x ) = tan( x ) and g ( x ) = cos( x ) x 2 - 3 . Find the domain of f + g multiplication: fg ( x ) = f ( x ) g ( x ) Ex. 2. Let f ( x ) = tan( x ) and g ( x ) = cos( x ) x 2 - 3 . Find the domain of fg division: f/g ( x ) = f ( x ) /g ( x ) Ex. 3. Let f ( x ) = tan( x ) and g ( x ) = cos( x ) x 2 - 3 . Find the domain of f/g 1
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2 Composition of functions Ex. 4. A spherical balloon is being inflated and the radius of the balloon is increasing at a rate of 2 cm/s. Express the radius r in terms of the time. Express the volume of the balloon in terms of the radius r . Express the volume of the balloon in terms of the time.
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3 Let f and g be two functions. Then the composition of f and g is defined by f g ( x ) = f ( g ( x )) . Ex. 5. Let f ( x ) = x 2 - 2 and g ( x ) = 4 x - 3 . Find f g and g f and their domains.
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4 Inverse functions Ex. 6. The high temperatures in Toronto between Dec. 15 and 25. Day Dec. 15 Dec. 16 Dec. 17 Dec. 18 Dec. 19 Dec. 20 Dec. 21 Temp. ( C ) 4 4 3 0 6 5 5 Ex. 7. The population of Burkina Faso, from 2007 to 2018 is given in the following table Year Population in million
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  • Fall '19
  • Exponentiation, Inverse function, Burkina Faso, Injective function, F G