Question

find the range of the function.

g(x) = 5 + (square root of) (4 - x)

please show all steps.

Answer 1

The range of a (real) function is limited by the quantity inside the square-root radical, namely 4-x≥0
Since the rest of the function is a polynomial, the above is the only limitation on the range.
Range of g(x) : (-∞ 4]