Answer:
-∞ < x < 1
Step-by-step explanation:
The equation f(x) = -(x - 1)² + 4 is a parabola that opens down with vertex in the point (1, 4).
This is because it has the form:
f(x) = a(x - h)² + k
Where the sign of a says if it opens up or down and (h, k) is the vertex.
Since the parabola opens down, it will be increasing until the vertex point and then it will be decreasing. The vertex point is (x, y) = (1, 4). So the interval where the function is increasing is: -∞ < x < 1