mid12003 - MATH 1300B-MIDTERM1-2003 Multiple Choice...

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Multiple Choice Section-Question 1 - Which of the following functions is the inverse of f ( x ) = 2 x +5 3 x - 4 ? A) f - 1 ( x ) = 4 x +5 3 x - 2 B) f - 1 ( x ) = 3 x - 4 2 x +5 C) f - 1 ( x ) = 5 - 2 x 4+3 x D) f - 1 ( x ) = 5 x - 2 4 x - 3 E) f - 1 ( x ) = 3 - 4 x 5+2 x Solution: (A) In f ( x ) = 2 x +5 3 x - 4 we replace x by y and f ( x ) by x , then x = 2 y + 5 3 y - 4 . Solve y we get y = f - 1 ( x ) = 4 x + 5 3 x - 2 . Question 2 - Consider the function f ( x ) = x 3 - x 2 - 9 x - 7 x +1 . Which of the following statements is true? A) lim x →- 1 f ( x ) does not exist B) lim x →- 1 f ( x ) = 4 C) lim x →- 1 f ( x ) = - 4 D) lim x →- 1 f ( x ) = 1 E) lim x →- 1 f ( x ) = 0 Solution: (C) The numerator can be written as x 3 - x 2 - 9 x - 7 = ( x + 1)( x 2 - 2 x - 7) . Thus lim x →- 1 f ( x ) = lim x →- 1 ( x 2 - 2 x - 7) = - 4 . Question 3 - Describe the interval(s) on which the following function f ( x ) = x + 2 x ( x + 1) is continuous: A) (0 , ) B) ( - 1 , 0) C) ( -∞

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mid12003 - MATH 1300B-MIDTERM1-2003 Multiple Choice...

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