Precalculus · Problem 28

Further Topics in Functions — Stitz & Zeager

Mathematics — Precalculus · inverse-functions

Problem

Let f(x)=2xx2−1f(x) = \dfrac{2x}{x^2-1}. Using the techniques in Section 4.2, graph y=f(x)y = f(x). Verify that ff is one-to-one on the interval (−1,1)(-1,1). Use the procedure outlined on Page 384 and your graphing calculator to find the formula for f−1(x)f^{-1}(x). Note that since f(0)=0f(0) = 0, it should be the case that f−1(0)=0f^{-1}(0) = 0. What goes wrong when you attempt to substitute x=0x = 0 into f−1(x)f^{-1}(x)? Discuss with your classmates how this problem arose and possible remedies.

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