quiz3Asol - Solutions to Quiz 3A...

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Unformatted text preview: Solutions to Quiz 3A www.math.ufl.edu/˜harringt January 24, 2008 1. Find the exact value of each expression: (a) log5 125 = log5 53 = 3 log5 5 = 3 (b) ln(1/e) = ln(1) − ln(e) = 0 − 1 = −1 √ 2. Find the inverse of f (x) = 3 − e2x and find the range of f −1 . (a) First we will find the inverse function. f (x) = y x x2 x2 − 3 3 − x2 ln(3 − x2 ) = = = = = = √ 3 − e2x √ 3 − e2y 3 − e2y −e2y e2y 2y 1 ln(3 − x2 ) = y 2 1 ln(3 − x2 ) f −1 (x) = 2 (b) Next we will find the range of f −1 by finding the domain of f . Recall that the range of f −1 is the same as the domain of f . Since f (x) = √ 3 − e2x then we need to find when 3 − e2x ≥ 0 3 − e2x 3 ln 3 1 ln 3 2 1 ≥0 ≥ e2x ≥ 2x ≥x So the range of f −1 is (−∞, 1 ln 3]. 2 3. The point P (1, 2) lies on the curve y = x2 + 1. If Q is the point (x, x2 + 1), then find the slope of the secant line for: (a) x = 0 Find the slope between P (1, 2) and Q(0, 1). So: m= 2−1 =1 1−0 (b) x = 2 Find the slope between P (1, 2) and Q(2, 5). So: m= 2 2−5 =3 1−2 ...
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This note was uploaded on 07/10/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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quiz3Asol - Solutions to Quiz 3A...

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