Let be a continuous and strictly increasing function on the closed interval with range

MATHEMATICS · Single correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Let ff be a continuous and strictly increasing function on the closed interval [a,b][a,b] with range [c,d][c,d]. Which of the following statements is true? (a) f−1f^{-1} is differentiable on (c,d)(c,d). (b) f−1f^{-1} is strictly decreasing on [c,d][c,d]. (c) f−1f^{-1} is continuous on [c,d][c,d]. (d) f−1f^{-1} may be discontinuous at cc or dd even though ff is continuous.

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