243 Review Exam 2(1) - MAT 243 REVIEW EXAM 2(1 Fill in the...

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MAT 243 REVIEW EXAM 2 (1) Fill in the blank in the statements below: (a) A function f : A B is one-to-one if and only if (b) A function f : A B is not one-to-one if and only if (c) A function f : A B is onto if and only if (d) A function f : A B is not onto if and only if (m) A sequence is a function whose domain (n) An arithmetic sequence is a whose domain (o) A geometric sequence is a whose domain (2) Prove that f : Z Z ; f ( n ) = 3 n - 5 is one-to-one but not onto. (3) Prove that g : R R + ∪ { 0 } ; g ( x ) = ( x + 3) 2 is not one-to-one but it is onto. 1
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2 MAT 243 REVIEW EXAM 2 (4) Let f : R R ; f ( x ) = x 2 . (a) Find f ([ - 3 , 2)). (b) Find f - 1 ((0 , 1)) (5) Let f : R R ; f ( x ) = sin x . (a) Find f ([ - π 6 , 0)). (b) Find f - 1 ( { 0 . 5 } ). (6) Let f : R R ; f ( x ) = b x 5 c . (a) Find f ([ - 1 , 11]). (b) Find f - 1 ( { 16 } ). (7) Evaluate the sum and simplify as much as possible. Show all your work. Calculator an-swers will not be accepted. (8) Evaluate the sum and simplify as much as possible. Show all your work. Calculator an- swers will not be accepted.
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  • Spring '06
  • Callahan
  • Math, Natural number, Geometric progression, Logarithm, Review Exam, Mohacsy

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