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Solution the composition f g is dened by f g

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Unformatted text preview: ne- to- one correspondence (bijection). The inverse function f −1 reverses the correspondence given by function f, therefore, f −1 (1) = c, f −1 (2) = a, and f −1 (3) = b. Ques\$ons Example 2: let f : Z → Z be such that f (x) = x + 1. Is f invertible, and if so, what is its inverse? Solution: the function f is invertible because it is a one- to- one correspondence (bijection). The inverse function f −1 reverses the correspondence so f −1 (y) = y – 1. - 2 … Z Z - 1 0 0 1 1 2 … - 1 Composi\$on Deﬁnition: let f : B → C , g : A → B. The composition of function f with function g, denoted by f o g, is a function from A to C deﬁned by Composi\$on A a b c d g B f C A V h a W i b X j Y c d C h i j Composi\$on Example 1: if and , then and Since f ( g (x) ) = f ( 2x+1 ) = ( 2x+1 )2 and g ( f (x) ) = g ( x2 ) = 2 (x2) +1 = 2 x2 +1 Composi\$on Ques\$ons Example 2: let g be the function from the set { a , b , c } to itself such that g (a) = b, g (b) = c, and g (c) = a. Let f be the function from the set { a , b , c } to the set {1 , 2 , 3 } s.t. f (a) = 3, f (b) = 2, and f (c) = 1. What are the compositions of f ∘ g and...
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