A function `phi(x)` satisfies the functional equation `x^2phi(x) + phi(1-x) = 2x-x^4` for all real `x`. Then `phi(x)` is given by

A function phi(x) satisfies the functional equation x^(2)phi(x)+phi(1-x)=2x-x^(4) for all real x. Then phi(x) is given by

A function phi(x) is called a primitive of f(x); if phi'(x)=f(x)

Let phi(a)=f(x)+f(2ax) and f'(x)>0 for all x in[0,a]. Then ,phi(x)

If phi(x) is polynomial function and phi(x)gtphi(x)AAxge1andphi(1)=0 ,then

If the function f(x) increases in the interval (a,b), and phi(x)[f(x)]^(2), then phi(x) increases in (a,b)phi(x) decreases in (a,b) we cannot say that phi(x) increases or decreases in (a,b). none of these

If phi(x) is a diferential real-valuted function satisfying phi'(x)+2phi(x)le1. prove that phi(x)-(1)/(2) is a non-incerasing function of x.

If phi(x) is a diferential real-valuted function satisfying phi'(x)+2phi(x)le1. prove that phi(x)-(1)/(2) is a non-incerasing function of x.

If phi(x) is a diferential real-valuted function satisfying phi'(x)+2phi(x)le1. prove that phi(x)-(1)/(2) is a non-incerasing function of x.