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If f(x) satisfies the relation 2f(x)+f(1...

If `f(x)` satisfies the relation `2f(x)+f(1-x)=x^2` for all real X, then f(x) is a)`(x^2+2x-1)/6` b)`(x^2+2x-1)/3` c)`(x^2+4x-1)/3` d)`(x^2-3x+1)/6`

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • If g(x) = x^2 +x -2 and 1/2 (gof) (x) = 2x^2 - 5x +2 , then f(x) is equal to a) 2x -3 b) 2x+3 c) 2x^2 +3x +1 d) 2x^2 -3x -1

    A
    `2x -3`
    B
    `2x+3`
    C
    `2x^2 +3x +1 `
    D
    `2x^2 -3x -1`

  • If f (x) = (x +2)/( 3x -1) , then f {f (x) } is

    A
    x
    B
    `-x`
    C
    `1/x`
    D
    `- 1/x`

  • If a function f satisfies f{f (x)}=x+1 for all real values of x and if f(0)=1/2 then f(1) is equal to a) 1/2 b)1 c) 3/2 d)2

    A
    `1/2`
    B
    1
    C
    `3/2`
    D
    2

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