(a) Suppose f is a one-to-one function with inverse f1, and that both f and f1 are differentiable. Use implicit differentiation to show that (f1)(x)=f(f1(x))1 provided that the denominator is not zero. (b) With the help of graphing software, sketch f(x)=x+ex. Using the graph, explain why it is plausible to conjecture that the inverse of f exists. (Be sure to clearly label your graph, and reference it in part (c) below. (c) Find f(x) and give a rough explanation of why certain characteristics of f(x) and f(x) indicate that f(x) is 1-to-1 and invertible. We will explore a more formal proof in the coming weeks when we have a few more tools at our disposal. (d) Use your formula from part (a) to evaluate (f1)(1), using f(x) as defined in part (b). (a) Suppose f is a one-to-one function with inverse f1, and that both f and f1 are differentiable. Use implicit differentiation to show that (f1)(x)=f(f1(x))1 provided that the denominator is not zero. (b) With the help of graphing software, sketch f(x)=x+ex. Using the graph, explain why it is plausible to conjecture that the inverse of f exists. (Be sure to clearly label your graph, and reference it in part (c) below. (c) Find f(x) and give a rough explanation of why certain characteristics of f(x) and f(x) indicate that f(x) is 1-to-1 and invertible. We will explore a more formal proof in the coming weeks when we have a few more tools at our disposal. (d) Use your formula from part (a) to evaluate (f1)(1), using f(x) as defined in part (b)