The domain the set of x values where the graph exists. In this case, f(x) is a rational function, which means that we have a numerator and a denominator. We know that if we set the denominator equal to zero, the function is undefined. We also have a square-root. The number under the square-root cannot be negative, otherwise the value will not be a real number.
So we have to set up our restrictions. The first one is the denominator, and the second one is the square-root.
√(2x + 5) - 8 = 0 and 2x + 5 ≥ 0
√(2x + 5) = 8 and 2x ≥ -5
2x + 5 = 64 and x ≥ -5/2
2x = 59 and x ≥ -2.5
x = 29.5 and x ≥ -2.5
This means that 29.5 and any value less than -2.5 are not in the domain.
The domain is [-2.5 , 29.5)∪(29.5 , ∞).