Find the range of f(x)= sqrt(x+1) + 4.

Expert Answers
justaguide eNotes educator| Certified Educator

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.]

samhouston eNotes educator| Certified Educator

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