Find domain and range?

Question

square root of x+5/x-1

Answer 1

I'll assume you mean √[(x+5)/(x-1)].

You can only take the square root of non-negative numbers, so (x+5)/(x-1) ≥ 0

That means the domain is (-∞,-5] U (1,∞).  We can include the 5 because it causes (x+5)/(x-1) = 0, but we can not include the 1 because (x+5)/(x-1) would be undefined.

The square root can never be negative, so we automatically have the range as all numbers greater than or equal to zero.

Are there any other values that it cannot take?

Yes, as x gets really large or small, (x+5)/(x-1) approaches 1.

That means √[(x+5)/(x-1)] approaches √1 = 1.

The range is [0,1) U (1,∞).