# Is it possible to solve this without guessing the function?

• Drao92
In summary, the conversation discusses finding the sum of f(1) and f(0) without knowing the function f(x). It is possible to solve this by considering f(f(f(x))) and showing that f(2^x-1) = 2^(f(x))-1. The function is injective, leading to the sum being 1. One person solved the function using differential equations, but the constant is unknown. The correct solution is f(1) + f(0) = 1, found by considering f(f(f(x))) and solving for f(1) and f(0) separately.
Drao92
We know f(f(x))=2^x-1;
We must calculate f(1)+f(0)
Its posible to solve this without guessing the function? If i derivate i get to f(0)=f(0) or f(1)=f(1).

Drao92 said:
We know f(f(x))=2^x-1;
We must calculate f(1)+f(0)
Its possible to solve this without guessing the function? If i derivate i get to f(0)=f(0) or f(1)=f(1).
What does derivate mean?

Yes, it's possible to solve without knowing what f(x) is.

Hint: Consider f(f(f(x))) to show that ##f(2^x-1) = 2^{f(x)}-1##.

Isnt f(2x-1)=2f(f(x))-1? And in this case it becamse very easy.
The hint leads me to f(0)=f(0)f(0)-1 , so f(0)=0 or 1.
Same result for f(1).
I guess the function is injective so the sum is 1?
Actually i solved the function but with diferential equation and obviously i don't know the constant :D.
Is this correct?
f(f(f(x)))=2^(f(f(x)))-1
f(f(f(x)))=f(2^x-1)=2^(f(f(x)))-1=f(2^x-1)=2^(2^x-1)-1
x=0=>f(2^0-1)=2^(2^0-1) -1<=>f(0)=0;
x=1=>f(2^1-1)=2^(2^1-1)-1<=>f(1)=1;
f(1)+f(0)=1;

Last edited:
How'd you get that?

No, sorry you are right. I messed up the argument of the function :D
Thanks, i understood .

Last edited:

## 1. Can a problem be solved without knowing the function?

Yes, it is possible to solve a problem without knowing the exact function. This can be done by using mathematical techniques such as trial and error, substitution, and elimination.

## 2. How can I solve a problem without guessing the function?

There are various methods that can be used to solve a problem without guessing the function. These include using algebraic manipulation, graphing techniques, and numerical approximation methods.

## 3. Is it necessary to know the function to solve a problem?

No, it is not always necessary to know the function to solve a problem. In many cases, the problem can be solved by analyzing the given data and using mathematical techniques to find the solution.

## 4. Are there any advantages to solving a problem without knowing the function?

Yes, solving a problem without knowing the function can have advantages such as improving problem-solving skills, promoting critical thinking, and expanding mathematical knowledge.

## 5. How do scientists solve complex problems without knowing the function?

Scientists use a combination of mathematical techniques and analytical thinking to solve complex problems without knowing the function. They also rely on their knowledge and experience in the field to guide them in finding the solution.

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