121616949-math.27 - a rectangular pen on three sides(with...

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1.3 Functions 13 10 25 30 0 10 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . t v Figure 1.7 A velocity function. Exercises Find the domain of each of the following functions: 1. y = f ( x ) = 2 x - 3 2. y = f ( x ) = 1 / ( x + 1) 3. y = f ( x ) = 1 / ( x 2 - 1) 4. y = f ( x ) = p - 1 /x 5. y = f ( x ) = 3 x 6. y = f ( x ) = 4 x 7. y = f ( x ) = p r 2 - ( x - h ) 2 , where r and h are positive constants. 8. y = f ( x ) = p 1 - (1 /x ) 9. y = f ( x ) = 1 / p 1 - (3 x ) 2 10. y = f ( x ) = x + 1 / ( x - 1) 11. y = f ( x ) = 1 / ( x - 1) 12. Find the domain of h ( x ) = ( x 2 - 9) / ( x - 3) x ± = 3 6 if x = 3. 13. Suppose f ( x ) = 3 x - 9 and g ( x ) = x . What is the domain of the composition ( g f )( x )? (Recall that composition is defined as ( g f )( x ) = g ( f ( x )).) What is the domain of ( f g )( x )? 14. A farmer wants to build a fence along a river. He has 500 feet of fencing and wants to enclose
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Unformatted text preview: a rectangular pen on three sides (with the river providing the fourth side). If x is the length of the side perpendicular to the river, determine the area of the pen as a function of x . What is the domain of this function? ⇒ 15. A can in the shape of a cylinder is to be made with a total of 100 square centimeters of material in the side, top, and bottom; the manufacturer wants the can to hold the maximum possible volume. Write the volume as a function of the radius r of the can; find the domain of the function. ⇒...
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