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Unformatted text preview: √ x ) 1 / 2 d) f ( x ) = sin ± cos x x ² b) g ( x ) = [( x 2 + 1) 2 + ( x 2 + 1) + 1] 2 e) g ( x ) = (sin 2 x )(sin x 2 )(sin 2 x 2 ) c) h ( x ) = ³ x − 2 x + sin x ´ − 1 f) h ( x ) = sin(cos x ) x 5. a) Prove that the formula for the derivative for an inverse function is ( f − 1 ) ( x ) = 1 f ( f − 1 ( x )) . (Hint: Let g ( x ) = f − 1 ( x ), then f ( g ( x )) = x . DiFerentiate.) b) ²ind f − 1 ( x ) given that f ( x ) = 2 x − 3 x +2 . c) DiFerentiate f − 1 ( x ) from part b) and compare with the derivative you get by applying the formula in part a). 6. ²ill in the table, given that h(x)=f(g(x)). a g ( a ) g ( a ) f ( a ) f ( a ) h ( a ) h ( a ) 1 3 221/3 1 27 2 2 d.n.e1 4 7. Sketch a graph for f , g , and h satisfying the table in Problem 6....
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This note was uploaded on 04/11/2011 for the course MATH 1400 taught by Professor Grether during the Spring '08 term at North Texas.
 Spring '08
 Grether

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