The number of integers in the domain of function, satisfying `f(x)+f(x^(-1))=(x^3+1)/x ,i s` (a) empty set (b) singleton set (c) Finite Set (d) An infinite set

Answer

2

Explanation

`f(x)+f((1)/(x))=x^(2)+(1)/(x)`
Replacing x by `(1)/(x),` we get `f((1)/(x))+f(x)=(1)/(x^(2))+x`
`or (1)/(x^(2))+x=x^(2)+(1)/(x)`
`or x-(1)/(x)=x^(2)-(1)/(x^(2))`
`or (x-(1)/(x))=(x-(1)/(x))(x+(1)/(x))`
` or (x-(1)/(x))(x+(1)/(x)-1)=0`
`x=(1)/(x), x+(1)/(x)=1`(rejected)
Hence, `x=1 or -1.`