Let f : R → R be a function defined by f(x)=-|x|3+|x|1+x2, then the graph of f (x) lies in which quadrant

Since, f (– x) = f (x)⇒ f (x) is an even function, its graph will be symmetrical about y-axis. Also, f(x)=−|x|3+|x|1+x2⇒ f (x) = –(positive) = negativei.e., the graph of f (x) completely lies below the x-axis, andis also symmetric about y-axis (as discussed above).∴ The graph of f (x) lies in III and IV quadrants.The correct option is (3)and (4)