APPM 1345 Midterm: appm1345spring2018exam3_sol
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Spring 2018: [14 pts] solve the following equations. (a) 2x2. Solution: (a) (b) log(x + 2) + log(x 1) = 1. 6x = 2 5 x2 6x = 5 x2 6x + 5 = 0 (x 5)(x 1) = 0 x = 1 or x = 5. Checking these potential solutions in the original equation shows that x = 4 is not a solution since we cannot take logarithms of negative numbers. 2. (a) [7 pts] using any method you choose, show that the function f (x) = (b) [7 pts] consider the function f (x) = x4 + x3 + 1 with x 0. Evaluate the derivative of f 1(x) at 3, that is, You can assume that f , with the restricted domain, is one-to-one. is one-to-one and nd its inverse. (cid:4) Solution: (a) using a graph: graph of f (x) passes the horizontal line test and is thus one-to-one. y.
