Find the range of f(x)= sqrt(x+1) + 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.]