since you cannot square root a negative, the smallest value for x is -1.
substitute -1 in for x.
sqrt(-1+1) + 4
sqrt(0) + 4
0 + 4
The range is greater than or equal to 4
The range of a function y = f(x) is all the real values that y can take while the value of x lies in the domain of the function. The domain of the function is all the values of x for which y is real.
Here f(x) = sqrt (x + 1) + 4
The square root is real only for non-negative numbers. This gives x + 1 >=0 or x lies in the interval [-1, inf.]
For values of x in the interval [-1, inf.], y has values in the interval [4, inf.]
The range of f(x) = sqrt(x + 1) + 4 is [4, inf.]