MATH 121 - WRITTEN EXERCISES-MODULE 5

# MATH 121 - WRITTEN EXERCISES-MODULE 5 - Jimmy...

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Jimmy Morgan-MAT-121-OL-(1 Nov 09 thru 23 Jan 2010 Module 5 Written Assignment 4.1 4.) Decide whether each function as defined or graphed is one-to-one. This graph is not one-to-one because any horizontal line will pass through more than one point. 12.) Decide whether each function as defined or graphed is one-to-one. 2 100 y x = - - 2 (1) 100 1 100 1 101 f = - - = - - = - 2 ( 1) 100 ( 1) 100 1 99 f - = - - - = - + = - This function is not one-to-one because any horizontal line will pass through more than one point. 16.) Decide whether each function as defined or graphed is one-to-one. 4 8 y x = - ; If x=0 y=-1/2 x=8 y=+/- infinity This function is one-to-one because any horizontal line will pass through only one point. 42.) Use the definition of inverses to determine whether f and g are inverses. 1 ( ) 3 9, ( ) 3 3 f x x g x x = + = -   1 ( )( ) ( ( )) 3( 3) 9 3 f g x f g x x = = - + o = 9 9 x - + = x 1 ( )( ) ( ( )) (3 9) 3 3 g f x g f x x = = + - o = 3 3 x + - = x Yes, function g is inverse of function f.

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Jimmy Morgan-MAT-121-OL-(1 Nov 09 thru 23 Jan 2010 4.1 (Con’t) 56.) For each function as defined that is one-to-one, (a) write an equation for the inverse function in the form 1 ( ) y f x - = , (b) graph f and 1 f - on the same axes, and (c) give the domain and the range of f and 1 f - . If the function is not one-to-one, say so. 4 5 y x = - 4 5 x y = - 4 5 y x = + 5 4 x y + = 1 1 5 ( ) 4 4 f x x - = + c. . Domain and Range of “ f ” and “ 1 f - ( 29 , -∞ ∞   64.) For each function as defined that is one-to-one, (a) write an equation for the inverse function in the form 1 ( ) y f x - = , (b) graph f and 1 f - on the same axes, and (c) give the domain and the range of f and 1 f - . If the function is not one-to-one, say so. 4 y x = = 4 4 ; x y y x = = a.) 1 4 ( ) f x x - = b.) c. Domain and Range of “ f ” and “ 1 f - ” are ( , 0) (0, ) -∞         4.2
Jimmy Morgan-MAT-121-OL-(1 Nov 09 thru 23 Jan 2010 24.) Graph each function. ( ) 2 x f x - = 52.) Solve each equation. ( ) 2

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MATH 121 - WRITTEN EXERCISES-MODULE 5 - Jimmy...

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