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If f(x) = a+bx, what are the real values of a and b such that f(f(f(1))) = 29 and f(f(f(0))) = 27

 Oct 16, 2018
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 f(f(f(x)))=a+b( a+b( a+bx))

 f(f(f(0)))=a+b(a+b(a))=27

 f(f(f(1)))=a+b(a+b(a+b))=29 

f(f(f(0)))=a+ba+b^2a=27

f(f(f(1)))=a+ba+ab^2+b^3=29

(1) a+ba+b^2a=27 -> f(f(f(1)))=(1)+b^3=29 so 27 + b^3 = 29 <=> b^3 = 29-27 <=> b^3 = 2 <=> b = \(\sqrt[3]{2}\)\(\)

 

 

after in f(f(f(1))) you are replacing and find the a!
 

 Oct 16, 2018

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