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studyguide- final (Math 121) - MATH 121 Final Exam Study...

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MATH 121 Final Exam Study Guide This is a list of problems to help you prepare for the final exam. It is not considered to be exhaustive and you should not expect to find your actual exam problems in the list below. It is to serve as a study aid and it cannot be a substitute for in-class reviews or study of your class notes. 1. Find all solutions to the equation: 3 x 2 5 x 2 = 0 2. Find the solution to the equation: x 3 2 x = x 2 1 that lies in the interval [0 , 1]. 3. The area of a right triangle is 24 and the hypotenuse has length 10. What are the lengths of the remaining sides? 4. A rectangle of perimeter 12 is inscribed in a circle of radius 5. What are the dimensions of the rectangle? 5. A train going from Chicago to Cleveland leaves at 10AM and travels at a speed of 60 miles per hour. A second train going from Cleveland to Chicago leaves at 12PM and travels at a speed of 55 miles per hour. If the cities are 500 miles apart, at what time do the trains meet and how far from Chicago do they meet? 6. Two cars leave from the same point. One car heads north at a speed of 30 miles per hour. The other car heads east at a speed of 35 mph. How far apart are the two cars after 30 minutes? 7. Compute the difference quotient, f ( x + h ) f ( x ) h , for the function f ( x ) = x 2 + x . 8. Find the domain of the function f ( x ) = x 1 4 x 2 . 9. Let f ( x ) = x 2 and g ( x ) = x + x + 2. (a) What is the domain of g ( x )? 1
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(b) Write the rule for the composite function g f . 10. Find the inverse of the function f ( x ) = 2 x 5 7 x + 4 . 11. Find the inverse of the function f ( x ) = 3 2 x 1 . 12. Find the remainder when the function f ( x ) = x 20 3 x 13 + 7 x + 1 is divided by the function g ( x ) = x + 1. 13. Show that the function g ( x ) = x 2 + 1 is a factor of the function f ( x ) = x 5 + x 2 x + 1.
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