Let `f(x)=1-x-x^3`.Find all real values of x satisfying the inequality, `1-f(x)-f^3(x)>f(1-5x)`

If f is symmetrical about x = 1, find the real values of x satisfying the equation f(x)=f((x+1)/(x+2)) .

Let f(x)=1-x-4x^(3),f:R rarr R then find the number of integrality satisfying the inequality 4f(x)^(3)+f(1-2x)+f(x)<1

Find all functions f satisfying the identity, f(x)+f((x-1)/x)=1+x,AA x inR-{0,1}

Let f:R-{3}rarr R be a real valued function satisfying the functional equation 3f(x)+2f((3x+5)/(x-3))=4x+2 Then f(x) is given as

Let f(x)=x+1 and phi(x)=x-2. Then the value of x satisfying |f(x)+phi(x)|=|f(x)|+|phi(x)| are :

if F(x)=x^2-2x+3 then the set of values of x satisfying f(x-1)=f(x+1)

Let f(x) be a polynomial function of degree n satisfying the condition f(x)f((1)/(x))=f(x)+f((1)/(x)). Find f(x)

Let f(x) be a real valued periodic function with domain R such that f(x+p)=1+[2-3f(x)+3(f(x))^(2)-(f(x))^(3)]^(1//3) hold good for all x in R and some positive constant p, then the periodic of f(x) is