100922 More problems on inverses

# If no explain why not b is the inverse of g also a

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. If no, explain why not. b. Is the inverse of g also a function? If yes, make a table of values and a graph for the inverse function g –1 . If no, explain why not. c. Let h ( x ) stand for the composite: h ( x ) = g ( f ( x )). Is the inverse of h also a function? If yes, make a table of values and a graph for the inverse function h –1 . If no, explain why not. 6. Here are some more inverses to calculate. a. Given f ( x ) = 3 3 1 x - , find f –1 ( x ). b. Given g ( x ) = 1 - x x , find g –1 ( x ). c. What was unusual about the answers to parts a and b ? (Look for something special that happened in these two answers, but not in most of the other inverses you’ve had to find.) 7. a. Given any one-to-one functions f and g , which one of these two statements must always be true? ( g f ) –1 = g –1 f –1 or ( g f ) –1 = f –1 g –1 Explain why your choice is correct. You might find it helpful to draw a diagram of functions as input-output machines. b. Find a similar fact about the inverse of a composite of three functions, ( h g f ) –1 .
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