MATH10560 Final: Math10560SolutionsPFinal
Document Summary
Question 1: let f (x) = e x 1 and let f 1 denote the inverse function. We have the formula (f 1) (a) = We apply this formula with a = e 2 1. Since f (2) = e 2 1, we have f 1(e 2 1) = 2. F (x) = e x , therefore f (2) = e 2. The formula says that (f 1) (e 2 1) = Question 2: solve the following equation for x: ln(x + 4) ln x = 1 . Amalgamating the logarithms, our equation becomes: ln x + 4 x = 1. Applying the exponential to both sides, we get. X + 4 x = e 1 = e. Multiplying both sides by x, we get x + 4 = ex and x ex = 4. Therefore x(1 e) = 4 and x = 4. Question 3: find the derivative of (x 2 + 1)x 2+1.
