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quiz 6 - g ◦ f It is the same as the codomain of the...

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CSE 260 QUIZ-6– Functions- ANSWER (20 minutes) NAME: 1. (6 points) Determine whether f is a function from Z + to R if (a) f ( x ) = 1 /x Yes (b) f ( n ) = n 2 + 1 Yes. 2. Consider the sets A = { 0 , 1 , 2 , 3 , 4 } and B = { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . Let f be a function from A to B , whose graph is G f = { (0 , 0) , (1 , 2) , (2 , 4) , (3 , 6) , (4 , 8) } (a) (3 points) Give the range of f . { 0 , 2 , 4 , 6 , 8 } (b) (3 points) If the inverse, f - 1 , exists, give it as a set of ordered pairs. If it does not exist, say why not. Inverse does not exist, because the function f is one to one but NOT onto. (c) ) Let g ( x ) = b x/ 2 c be a function from B to A . i. (3 points) Give the domain of the composition function g f . Domain of g f is the same as that of f: A = { 0 , 1 , 2 , 3 , 4 } ii. (3 points) Give the codomain of
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Unformatted text preview: g ◦ f . It is the same as the codomain of the function g: A = { , 1 , 2 , 3 , 4 } iii. (6 points) Give the graph of g ◦ f as a set of ordered pairs. { ((0 , 0) , (1 , 1) , (2 , 2) , (3 , 3) , (4 , 4) } 3. (6 points) Find the inverse function of f if it exists. f : R → R , f ( x ) = x/ 2 + 1 This function is one-to-one and onto. One-to-one: ( f ( x 1 ) 6 = f ( x 2 )) → (( x 1 / 2 + 1) 6 = ( x 2 / 2 + 1)) → ( x 1 6 = x 2 ) y = x/ 2 + 1 x = 2( y-1) f-1 ( x ) = 2( x-1)...
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