Given:
The graph of f(x).
To find:
The interval where f(x)>0.
Solution:
From the given graph it is clear that the graph of f(x) lies above the axis for the intervals (-4,-1) and (1,∞), so f(x)>0 for [tex]-4<x<-1[/tex] and [tex]1<x<\infty[/tex].
The graph of f(x) lies below the axis for the intervals (-∞,-4) and (-1,1), so f(x)<0 for [tex]-\infty<x<-4[/tex] and [tex]-1<x<1[/tex].
Form the given options, interval [tex]-2<x<-1[/tex] is the only interval for which the function lies above the x-axis.
Therefore, the correct option is A.
