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MT 1 w sln

# MT 1 w sln - Prof Haiman Math 1ACalculus First Midterm Exam...

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Prof. Haiman Math 1A—Calculus Fall, 2006 First Midterm Exam Solutions Name Student ID Number Section time and Instructor You may use one sheet of notes. No other notes, books or calculators allowed. There are 10 questions, on front and back. Write answers on the exam and turn in only this paper. Show enough work so that we can see how you arrived at your answers. 1. Write a formula for the function whose graph is shown. Assume the lines continue to infinity outside the part of the graph shown here, and that their slopes are simple fractions. x y f ( x ) = - x x < 1 , ( x + 1) / 2 x 1 2. If f ( x ) = 2 x , g ( x ) = 1 /x , and h ( x ) = x + 5, find f g h . f g h ( x ) = 2 x + 5 . 3. Which of the following are 1-1 functions? (a) f ( x ) = x 3 , for all real numbers x (b) f ( x ) = x 4 , for all real numbers x (c) f ( x ) = x 3 , for x 0 (d) f ( x ) = x 4 , for x 0 All except (b). 4. Find the inverse function of f ( x ) = 3 sin( x + ( π/ 4)). f - 1 ( x ) = sin - 1 ( x/ 3) - π/ 4. 5. Simplify 16 log 2 ( x ) . 16 log 2 ( x ) = 2 4 log 2 ( x ) = 2 log 2 ( x 4 ) = x 4 . Strictly speaking, this is valid only for x > 0.

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MT 1 w sln - Prof Haiman Math 1ACalculus First Midterm Exam...

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