a function f is continuous on [-1,1] and some of the values of f are shown below: If f (x) =0 has only one solution, r <0, then a possible value of b is

Question

Table is : (-1,2), (0,b), (1,-2)

Answer 1

Best to draw a sketch of the f(x). In the negative region of x where -1<x<0, we have two defined points, (-1,2) and (r,0). In the positive region of x where 0<x<1 there is only one point (1,-2). Since there is only one root, r, f(x) cannot cross the x axis again and must continue negative until f(1)=-2. Therefore f(x) intersects the y axis (x=0) at b, making b<0 (y intercept), where y=f(x). So the solution is b<0.