The number of integers in the domain of function, satisfying f(x)+fx−1=x3+1x, is ______.

f(x)+f1x=x2+1x Replacing x by 1x, we get f1x+f(x)=1x2+xor  1x2+x=x2+1xor  x−1x=x2−1x2or  x−1x=x−1xx+1xor  x−1xx+1x−1=0x=1x; x+1x=1 (rejected)  Hence, x=1 or −1.