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Question

Given a function #f(x)# = #4x-7# , find the value of k such that #2f^-1(k)# = #f (-1)#

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Answer 1 · 2017-08-29T05:36:39

#k=-29#

We have #f(x)=4x-7# i.e. #x=1/4(f(x)+7)=1/4f(x)+7/4#

Therefore #f^(-1)(x)=1/4x+7/4#

and #2f^(-1)(k)=1/2k+7/2#

But #2f^(-1)(k)=f(-1)=-4-7=-11#

Hence #1/2k+7/2=-11# i.e. #1/2k=-11-7/2=-29/2#

and #k=-29#