Home
Class 12
MATHS
A function phi(x) satisfies the function...

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

`x^2`

B

`1-x^2`

C

`1+x^2`

D

`x^2+x+1`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 2

    KVPY PREVIOUS YEAR|Exercise EXERCISE|25 Videos

  • MOCK TEST 4

    KVPY PREVIOUS YEAR|Exercise EXERCISE|25 Videos

Similar Questions

Explore conceptually related problems

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 the solution of the differential equation x(dy)/(dx)+y=xe^(x) be xy=phi(x)+c then phi(x) is:

Let f(x)=tan^(-1){phi(x)}, where phi(x) is m*i for 0

The solution of the differential equation (dy)/(dx) = (y phi ' (x) - y^(2))/(phi (x)) is :

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

KVPY PREVIOUS YEAR-MOCK TEST 3-EXERCISE
  1. If f: R to R, g , R to R be two funcitons, and h(x) = 2 "min" {f(x) - ...

    Text Solution

    |

  2. The area bounded by the curves y=|x|-1a n dy=-|x|+1 is 1 b. 2 c. 2s...

    Text Solution

    |

  3. A function phi(x) satisfies the functional equation x^2phi(x) + phi(1-...

    Text Solution

    |

  4. If n is a natural number,then

    Text Solution

    |

  5. Let S(n)=underset(k=1)overset(n)sum (n)/(n^(2)+nk+k^(2)) and T(n)=unde...

    Text Solution

    |

  6. Two friends visit a restaurant randomly during 5 pm to 6 pm . Among...

    Text Solution

    |

  7. For any n in N, the value of the expression sqrt(2+sqrt(2+sqrt(2+.......

    Text Solution

    |

  8. If a, b and c are distinct positive numbers, then the expression (a + ...

    Text Solution

    |

  9. The general value of theta satisfying the equation 2sin^(2)theta-3sint...

    Text Solution

    |

  10. For 3 xx 3 matrices M and N, which of the following statement(s) is/ar...

    Text Solution

    |

  11. If the inequality (m x^2+3x+4+2x)//(x^2+2x+2)<5 is satisfied for all x...

    Text Solution

    |

  12. If f(x)=g(x^(3))+xh(x^(3)) is divisiblel by x^(2)+x+1, then

    Text Solution

    |

  13. The area of the trapezium whose vertices lie on the parabola y^2 = 4x ...

    Text Solution

    |

  14. A person goes to office either by car, scooter, bus or train probabili...

    Text Solution

    |

  15. The line x+ y = 1 meets X-axis at A and Y-axis at B,P is the mid-poin...

    Text Solution

    |

  16. If x,y andz are three real numbers such that x+y+z=4 and x^2+y^2+z^2=6...

    Text Solution

    |

  17. A variable point P on the ellipse of eccentricity e is joined to the f...

    Text Solution

    |

  18. Letz,z0be two complex numbers z0being the cojugate of z0. The numbers ...

    Text Solution

    |

  19. A person throws dice, one the common cube and the other reglowest tera...

    Text Solution

    |

  20. The integers x,y and z each are perfect squares and x>y>z>0.If x,y,z f...

    Text Solution

    |