The-tangent-line-to-y-f-x-at-3-4-is-given-y-3x-5-What-is-the-tangent-line-to-y-f-1-x-at-3-4-where-f-x-is-an-injective-continous-function-that-satisfies-f-3-4-

Question Number 121766 by liberty last updated on 11/Nov/20

$$\mathrm{The}\:\mathrm{tangent}\:\mathrm{line}\:\mathrm{to}\:\mathrm{y}\:=\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{at}\:\left(\mathrm{3},\mathrm{4}\right)\:\mathrm{is} \\ $$$$\mathrm{given}\:\mathrm{y}=\mathrm{3x}−\mathrm{5}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{tangent}\:\mathrm{line} \\ $$$$\mathrm{to}\:\mathrm{y}\:=\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)\:\mathrm{at}\:\left(\mathrm{3},\mathrm{4}\right)\:\mathrm{where}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{is}\:\mathrm{an} \\ $$$$\mathrm{injective}\:\mathrm{continous}\:\mathrm{function}\:\mathrm{that}\:\mathrm{satisfies} \\ $$$$\mathrm{f}\left(\mathrm{3}\right)=\mathrm{4}. \\ $$

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