h2 - ( { y : 0 ≤ y ≤ 1 } ), if exists, where f-1 ( Y )...

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[40] Homework 2. Language of Mathematics Each problem is worth 10 points [10] Prove A B = ¯ A ¯ B without using the de Morgan law and Venn’s diagrams. [10] What is the image of f ( R ), where R is the set of all reals: f ( x ) = x 4 f ( x ) = x 2 - 4 x f ( x ) = 2 x 2 f ( x ) = sin( x ) [10] Is f ( x ) = x 2 + 1 a bijection of R R ? Compute also f - 1
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Unformatted text preview: ( { y : 0 ≤ y ≤ 1 } ), if exists, where f-1 ( Y ) denotes an inverse image, that is, the set of all x such that f ( x ) ∈ Y . [10] What are the values of the following: 99 s i =5 5 · 2 i-4 , 100 s j =3 (2 j +1-2 j ) , 100 p k =1 (-1) k . 1...
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This note was uploaded on 03/26/2012 for the course STAT 350 taught by Professor Staff during the Spring '08 term at Purdue.

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