Domain of function

Question

For the function √x / 1-x , why is the domain (1,positive infinity)? 

 

I know you cant have 0 in the denominator but I thought you can count everything above 0 like 0.1,0.2 etc.

Answer 1

Hi Alex,

 

I assume your function is

 

f(x) = √x / (1 - x)

 

You really need to insert the parentheses to make the function correct. This is in line with the order of operations in Algebra.

 

Given that this is the true form of the function, the domain is all values that you can legally insert for x. The range is all values that f(x) can take on.

 

You have two limitations on x. First of all, the square root prevents x from being negative, provided you wish to keep f(x) real valued. You also have the restriction that x cannot be 1 otherwise you have a divide-by-zero problem. To me, the domain should be

 

D = [0, 1) ∪ (1, ∞)

 

where the ∪ sign means union. It is perfectly okay to have numbers between 0 and 1, including 0, in your domain. Your proposed answer is missing that.

 

Is your f(x) restricted to be positive?