MATH 19 Midterm: MATH 19 Exam 1 Winter 2011
Document Summary
Consider the function y = f (x) = ex. We must exclude the possibility that 1+2ex = 0. 2 , which is impossible since ex > 0. But this would mean ex = 1 for all x. Compute f 1, the inverse of f . We solve for x in the formula for f above. y = ex. 1 + 2ex (1 + 2ex)y = ex y + 2yex = ex y = ex 2yex y = (1 2y)ex ex = y. So the inverse function is f 1(x) = ln(cid:0) x. Solution: that the range of f is the domain of f 1. The easy way to do this problem is to remember x. > 0 in order for the natural log to make sense. Drawing a number line one may check that this occurs for (0, 1. 1: (10 points) determine the following limits of the function f (x) whose graph is given above.
