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Quiz 2 Math 1050-002 (Summer 2002) Tuesday , June 4 , 2002 Name: 1 Student ID: ? Show all your works for full/partial credit. 1. (5 pts) Find the equation of line passing through the points, (4, 3), (−4, −4) 7 ANSWER: Slope is 3−(−4) 4−(−4) = 7/8. Now we have an equatuin of y = 8 x + b. To find b, put one point (4, 3) into the equation. That is, 3 = 78 (4) + b , so that b = − 12 . The equation is y = 78 x − 12 2. (5 pts) If a function is given by f (x) = 1 x+1 , then what are the values of f (0), f ( 12 ), and f (x3 ) ? ANSWER: f (0) = 1, f ( 12 ) = 1 1/2+1 = 23 , f (x3 ) = 1 . x3 +1 3. (5 pts) Determine whether the given function is even, odd, or neither. Use the definition of even and odd function to verify your conclusion. f (x) = x4 + x2 + 3 ANSWER: f (−x) = (−x)4 + (−x)2 + 3 = x4 + x2 + 3 = f (x). It is an even function by the definition. 4. (5 pts) What is the inverse function of f (x) = 5x ? Verify that f (f −1 (x)) = x . ANSWER: Its inverse function is 15 x. It is shown as f (f −1 (x)) = f ( 15 x) = 5 15 x = x.