Answer:
b. [tex](-1,0)\cup (1,\infty)[/tex]
Step-by-step explanation:
The graph can be divided into 4 regions.
Region 1 is for [tex]x\in (-\infty,-1)[/tex]
Region 2 is for [tex]x\in (-1,0)[/tex]
Region 3 is for [tex]x\in (0,1)[/tex]
Region 4 is for [tex]x\in (1,\infty)[/tex]
So, for the region 1, the values of [tex]y[/tex] goes on decreasing with increasing [tex]x[/tex]. Therefore, the function is decreasing in the interval [tex](-\infty,-1)[/tex].
Now, for the region 2, the values of [tex]y[/tex] increases with increasing [tex]x[/tex]. So, the function is increasing in the interval [tex](-1,0)[/tex].
For the region 3, the the values of [tex]y[/tex] goes on decreasing with increasing [tex]x[/tex]. Therefore, the function is decreasing in the interval [tex](0,1)[/tex].
Now, for the region 4, the values of [tex]y[/tex] increases with increasing [tex]x[/tex]. So, the function is increasing in the interval [tex](1,\infty)[/tex].
Therefore, regions 2 and 4 are the regions when the function is increasing.
Hence, the correct option is b. [tex](-1,0)\cup (1,\infty)[/tex]