SOLUTION: If f(x)=3x+11, what is the value of (f^-1 o f)(2)....I don't even know where to start on this one!!!

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 Algebra: Functions, Domain, NOT graphing Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Functions Question 22602: If f(x)=3x+11, what is the value of (f^-1 o f)(2)....I don't even know where to start on this one!!!Answer by venugopalramana(3286)   (Show Source): You can put this solution on YOUR website!If f(x)=3x+11, what is the value of (f^-1 o f)(2)....I don't even know where to start on this one!!! LET ME TELL YOU FEW THINGS FIRST...IF F(X)=3X+11...THEN F(2) MEANS PUT 2 INPLACE OF X ...YOU GET F(2)=3*2+11=17 F^-1(X) MEANS LIKE THIS ..CALL Y=F(X)=3X+11 AS GIVEN ..THEN YOU HAVE TO FIND X INTERMS OF Y.AS WE HAVE 3X=Y-11 X=(Y-11)/3...THIS FUNCTION (Y-11)/3 IS CALLED F^-1(X) = F(Y)=(Y-11)/3 SO F(X) AND F^-1(X ARE INVERSE PROCESSES.SO IF YOU APPLY BOTH TO SOME X YOU GET BACK X..THAT IS F^-1 OF F(X)=X..LET US CJHECK WITH OUR EXAMPLE.. F(X)=3X+11..SO F^-1{3X+11)= {PUT 3X+11 IN PLACE OF Y SINCE F^-1(X)=F(Y)=(Y-11)/3 ..SO WE GET (3X+11-11)/3=3X/3=X...... IN THE PRESENT PROBLEM..... F(X)=3X+11....SO F(2)=3*2+11=17 F^-1(X)=F(Y)=(Y-11)/3....SO F^-1(F(2))=F^-1(17)=(17-11)/3=6/3=2...SO WE GET BACK OUR X=2 AS THE ANSWER AS PROVED ABOVE....