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Unformatted text preview: (b) f ( x ) = 1 x 2 − 4 x + 3 6. Sketch the graph of the piecewise deﬁned function f ( x ) = x 2 if x < 1 x 3 if x ≥ 1 and ﬁnd f (0) , f (1) , f (2) . 7. Sketch the graph of the function f ( x ) = − x − 1  + 2 , not by plotting points, but by starting with the graph of a standard function and applying transformations. 8. Show that the equation x 2 + y 2 + 8 x − 4 y + 3 = 0 represents a circle, and ﬁnd the center and radius of the circle. 9. Find the maximum or minimum value of the function y = x 2 − 2 x + 2 . 10. Use f ( x ) = √ 1 − x and g ( x ) = 1 x 2 + 1 to ﬁnd (a) f ◦ g (b) g ◦ f (c) f ◦ f (d) g ◦ g (e) fg (f) f/g 11. Find the inverse of the following functions: (a) f ( x ) = x x − 2 (b) f ( x ) = 1 + 2 x 3...
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This note was uploaded on 02/27/2012 for the course MATH 8650 taught by Professor Kiryltsishchanka during the Spring '12 term at NYU.
 Spring '12
 KIRYLTSISHCHANKA
 Calculus, Algebra, Equations

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