?A function and its inverse function The function \(f(x)=\frac{x}{x+1}\) is one-to-one

Chapter 7, Problem 221

(choose chapter or problem)

A function and its inverse function The function \(f(x)=\frac{x}{x+1}\) is one-to-one for x > -1 and has an inverse on that interval.

a. Graph f for x > -1.

b. Find the inverse function \(f^{-1}\) corresponding to the function graphed in part (a). Graph \(f^{-1}\) on the same set of axes as in part (a).

c. Evaluate the derivative of \(f^{-1}\) at the point \(\left(\frac{1}{2},\ 1\right)\).

d. Sketch the tangent lines on the graphs of f and \(f^{-1}\) at \(\left(1,\ \frac{1}{2}\right)\) and \(\left(\frac{1}{2},\ 1\right)\), respectively.