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

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

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

Are the following functions identical ? f(x) = log ( x-2) + log (x-3) and phi (x) log (x-2) (x-3)

If a function f(x) increases in the interval (a,b). then the function phi(x)=[f(x)]^(n) increases in the same interval and phi(x)!=f(x) if

Let f(x+y)=f(x)*f(y)AA x,y in R and f(0)!=0* Then the function phi defined by .Then the function phi(x)=(f(x))/(1+(f(x))^(2)) is

In what interval are the following functions identical? (a) f(x)=x and phi (x)=10^(log x) . (b) f(x)=sqrtx sqrt(x-1) and phi (x)=sqrt(x(x-1)) .

Are the following functions identical? (a) f(x)=x/x and phi (x)=1 (b) f(x)=x and phi (x)=(sqrtx)^(2) , (c) f(x)=1 and phi (x)=sin^(2) x+cos^(2) x (d) f(x)=log (x-1)+log(x-2) and phi(x)=log(x-1) (x-2)

Are the following functions identical ? f (x) = x and phi (x) = ( sqrt"" x)^2

If phi(x) is a polynomial function and phi'(x)>phi(x)AA x>=1 and phi(1)=0, then phi(x)>=0AA x>=1 phi(x) =1phi(x)=0AA x>=1 (d) none of these