To find the range of the function g(x) = -2f(x) + 1, we need to consider the range of the original function f(x) and then apply the given transformation.
1. Let's assume f(x) has a range of Rf.
2. The function g(x) = -2f(x) + 1 will take the values of -2 times each value in the range of f(x) and then add 1.
3. Multiplying by -2 reflects the values in the range of f(x) across the x-axis and compresses them by a factor of 2. Adding 1 shifts the reflected and compressed values up by 1 unit.
4. If Rf is the range of f(x), then the range of g(x) will be -2Rf + 1.
Therefore, the correct answer would be:
C. (-2, ∞)
