If f(x) satisfies the relation 2f(x) +f(...

If `f(x)` satisfies the relation `2f(x) +f(1-x)=x^2` for all real x, then find f(x).

A

`(x^(2)+2x-1)/(6)`

B

`(x^(2)+2x-1)/(3)`

C

`(x^(2)+4x-1)/(3)`

D

`(x^(2)-3x+1)/(6)`

Verified by Experts

The correct Answer is:

B

Similar Questions

Explore conceptually related problems

If f(x) satisfies the relation 2f(x)+(1-x)=x^(2) for all real x, then find f(x) .

If f(x) satisfies the relation f(x)+f(x+4)=f(x+2)+f(x+6) for all x, then prove that f(x) is periodic and find its period.

If a real valued function f(x) satisfies the equation f(x+y)=f(x)+f(y) for all x,y in R then f(x) is

If a real function f(x) satisfies the relation f(x) = f(2a -x) for all x in R . Then, its graph is symmetrical about the line.

A function f(x) satisfies the functional equation x^(2)f(x)+f(1-x)=2x-x^(4) for all real x.f(x) must be

If function f satisfies the relation f(x)*f'(-x)=f(-x)*f'(x) for all x and f(0)=3, and if f(3)=3, then the value of f(-3) is

If a real polynomial of degree n satisfies the relation f(x)=f(x)f''(x)"for all "x in R" Then "f"R to R

Function f satisfies the relation f(x)+2f((1)/(1-x))=x AA x in R-{1,0} then f(2) is equal to

A polynomial function f(x) satisfies the condition f(x)f((1)/(x))=f(x)+f((1)/(x)) for all x in R,x!=0. If f(3)=-26, then f(4)=

A function f (x) which satisfies, f ' (sin ^(2)x) = cos ^(2) x for all real x & f (1)=1 is