analytically determine the range of the function for f(x) = 2^x+2^(-x)?

[Aaron17]

Hi, how can I analytically determine the range of the function for f(x) = 2^x+2^(-x)?

If I have an ordinary linear equation, I proceed as follows: f(x) = x+2 => y=x+2 =>x=y-2== range of function But I don't see what to do here

 

[Deleted member 4993]

Hi, how can I analytically determine the range of the function for f(x) = 2^x+2^(-x)?

If I have an ordinary linear equation, I proceed as follows: f(x) = x+2 => y=x+2 y-2 = x == range of function But I don't see what to do here

I think you have a confusion regarding the definition of "range of a function".

Please do a Google search with key-words "definition of range of a function" and tell us what you found.

 

[Aaron17]

I am speaking about this, sorry i dont know how to translate it

 

[Deleted member 4993]

I am speaking about this, sorry i dont know how to translate itView attachment 34364

Correct

Range is all the values that a function can achieve within a given domain.

I am assuming that the domain of your function is -∞ to +∞ [is it given in the problem and you forgot to mention it ?]

[Hint} You know for real numbers (a & b), a^b is always positive.

Now what....

 

[Dr.Peterson]

Hi, how can I analytically determine the range of the function for f(x) = 2^x+2^(-x)?

If I have an ordinary linear equation, I proceed as follows: f(x) = x+2 => y=x+2 =>x=y-2== range of function But I don't see what to do here

You say "analytically", and put this under calculus; have you differentiated to find the minimum or maximum yet?

And have you checked for symmetry, which may help visualize it?

Or, if by "analytically" you mean "algebraically", using the inverse as in your example, have you tried to find the inverse/solve for x? It can be done.

(Hint: Let u = 2^x.)

 

[Steven G]

What is the range of y=2^x?
What is the range of y =2^(-x) = (1/2)^x?
What is the range of y = 2^x + (1/2)^x?