Final answer:
The range of the function f(x) = -1/√(2 - x) is all real numbers less than 2, because as x approaches 2 from the left, the function output grows without bound negatively but never reaches zero.
Step-by-step explanation:
To find the range of the function f(x) = -1/√(2 - x), we need to consider the domain first since the range is dependent on the values that x can take. The function contains a square root in the denominator, and because the square root of a negative number is not defined in the set of real numbers, we must have 2 - x > 0. Simplifying this inequality gives us x < 2. So the domain of f(x) is all real numbers less than 2.
The function will yield real number outputs for all x in this domain, but because the square root function grows without bound and the negative sign flips the reciprocal, f(x) will have all real numbers as its range except for zero, since the function tends towards negative infinity as x approaches 2 from the left, but it will never actually reach 0. Hence the correct option for the range of f(x) is d) x < 2.