For `x in R`, the functions f(x) satisfies `2f(x)+f(1-x)=x^(2)`. The value of f(4) is equal to

For x in R-{1}, the function f(x) satisfies f(x)+2f((1)/(1-x))=x. Find f(2)

A real valued function f:R rarr R satisfies f(x)+f(5x+y)+6xy=f(9x-y)+18x^(2)+4 Then the value of f(4) is equal to

If the function f(x) satisfies lim_(x to 1) (f(x)-2)/(x^(2)-1)=pi , then lim_(x to 1)f(x) is equal to

Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be a function that satisfies f(x)+g(x)=x^(2) . Then the value of the integral int_(0)^(1) f(x)g(x) dx is equal to -

If the function f: R to R is defined by f(x)=x^(2)-6x-14 , then f^(-1)(2) is equal to -

For x in R-{0,1}, " let " f_(1)(x)=(1)/(x), f_(2)(x)=1-x and f_(3)(x)=(1)/(1-x) be three given functions. If a function, J(x) satisfies (f_(2) @J@f_(1))(x)=f_(3)(x), " then " J(x) is equal to

For x in R-{0,1}, " let " f_(1)(x)=(1)/(x), f_(2)(x)=1-x and f_(3)(x)=(1)/(1-x) be three given functions. If a function, J(x) satisfies (f_(2) @J@f_(1))(x)=f_(3)(x), " then " J(x) is equal to

Let a function f(x) satisfies f(x)+f(2x)+f(2-x)+f(1+x)=x,AA x in R Then find the value of f(0)

If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x) , then period of f(x) can be