If the range of the function f(x)=x^2 is {25,36}, then what is the domain?

Question

Please break down the problem because I am honestly so confused, thanks! 

Answer 1

No problem! Just work backward:

 25 = X²

±√25 = √X²                                   Remember -- if you take a root that wasn't there before, it can be plus or minus

 - 5 ≤ X ≤ 5

Repeat with the 36, and you will get:

 - 6 ≤ X ≤ 6

Here is the weird part: you will get a range in parts:

[-6, -5] U [5, 6]                             This is because your answers can't be smaller than 25 or above 36, you have to stay between the two domains.