HelloWorld

Don't forget 49

I think your calculation is incorrect, the answer I got is \(\frac{1}{\lfloor \sqrt[4]{2016} \rfloor}\)

I don't think I understand this question, isn't the function f_n always defined for [0,1]? Am I missing something?

No problem 

the equation is 3^2x+2+27^x+1=36, not 3*(2x+2)+27*(x+1)=36. 

you got from 3^2(x+1) + 3^3(x+1) = 3² * 4 to 1^x+1 + 3^x+1 = 4. Check your answer, you divided the right side by 9 and the left side by (3²)^x+1=9^x+1.

I think this can be further simplified:

(2x+x²) /(24x+8x²)=(2+x)/(24+8x) (when x!=0)

EP on the right side you divide by 9 and on the left side you divide by 9^x+1, you can't do that

You can't divide by 3² like that

I don't think your factoring is correct, the equation

(3²)^x+1 + (3³)^x+1 =(3²)^x+1*(1+3)

Is not always true (although the only solution is x=0)