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Let-g-R-R-be-given-by-g-x-3-4x-Prove-by-induction-that-for-all-positive-integers-n-g-n-x-4-n-1-4-n-x-If-for-every-positive-integer-k-we-inteprete-g-k-as-the-inverse-of-the-fu




Question Number 145641 by physicstutes last updated on 06/Jul/21
Let g:R→R be given by g(x) = 3 + 4x .Prove by induction  that, for all positive integers n,   g^n (x) = (4^n −1) + 4^n (x).  If for every positive integer k, we inteprete g^(−k)  as the inverse  of the function g^k .Prove that the above formula holds alsl  for all negative integers n.
Letg:RRbegivenbyg(x)=3+4x.Provebyinductionthat,forallpositiveintegersn,gn(x)=(4n1)+4n(x).Ifforeverypositiveintegerk,weintepretegkastheinverseofthefunctiongk.Provethattheaboveformulaholdsalslforallnegativeintegersn.

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