Home
Class 12
MATHS
If f(x) + 2f(1 - x) =x^2 + 2, forall x i...

If f(x) + 2f(1 - x) =`x^2 + 2, forall x in R`, then f(x) is

A

m=13, M=24

B

m=1/4, M=1/2

C

m=-11, M=0

D

m=1, M=12

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY & DIFFERENTIABILITY

    PATHFINDER|Exercise QUESTION BANK|13 Videos
  • DETERMINATES

    PATHFINDER|Exercise QUESTION BANK|21 Videos

Similar Questions

Explore conceptually related problems

f(x) is real valued function such that 2f(x) + 3f(-x) = 15 - 4x for all x in R . Then f(2) =

If f(x + y) = f(x) - f(y), forall x, y in R , then show that f(3) = f(1)

If the function f: R to R is defined by f(x) =(x^(2)+1)^(35) for all x in RR then f is

If f(x)=1/3{f(x+1)+5/(f(x+2)}} and f(x) gt 0 for all x in R , then lim_(x rarr infty)f(x) is

If 2f(x) - 3f(1/x) = x^2 (x ne 0) , then find f(2).

f is a function such that f(x + y) = f(x) .f(y), forall x, y in R , if f(1) = 3, then find sum_(r = 1)^n f(r) .

Let f(x+p)=1+{2-3f(x)+3(f(x))^2-(f(x)^3}^(1//3), for all x in R where p>0 , then prove f(x) is periodic.

Let f be a function such that f(x + y) = f(x) + f(y) forall x , y in R , if f(1) = k, then show that f(n) is equal to nk.

If f(x+1/2)+f(x-1/2)=f(x)fora l lx in R , then the period of f(x) is (a) 1 (b) 2 (c) 3 (d) 4

PATHFINDER-DEFINITE INTEGRATION-QUESTION BANK
  1. Let f: R rarr R be a continuous odd function, which vanishes exactly a...

    Text Solution

    |

  2. Let f(x)=7tan^8x+7tan^6x-3tan^4x-3tan^2x for all x in (-pi/2, pi/2). T...

    Text Solution

    |

  3. If f(x) + 2f(1 - x) =x^2 + 2, forall x in R, then f(x) is

    Text Solution

    |

  4. The option(s) with the values of a and L that satisfy the following eq...

    Text Solution

    |

  5. Let F:RrarrR be a thrice differentiable function. Suppose that F(1)=0,...

    Text Solution

    |

  6. The integral int2^4 (logx^2)/((logx^2)+log(36-12x+x^2)) dx is equal to...

    Text Solution

    |

  7. Let xn = (1 - 1/3)^2 (1-1/6)^2 (1-1/10)^2 ...... (1 - 1/((n(n + 1))/2)...

    Text Solution

    |

  8. underset(nrarrinfty)lim (sqrt1+sqrt2+.......+sqrt(n-1))/(nsqrtn) = ?

    Text Solution

    |

  9. Let f : Rrarr R be a continuous function which satisfies f(x) = int0^x...

    Text Solution

    |

  10. Let xn = (1 - 1/3)^2 (1-1/6)^2 (1-1/10)^2 ...... (1 - 1/((n(n + 1))/2)...

    Text Solution

    |

  11. Let f(x) denote the fractional part of a real number x. Then the value...

    Text Solution

    |

  12. Let f : (0,infty) rarr R be given by f(x) = int(1/x)^(x) e^-(t + 1/t...

    Text Solution

    |

  13. Let f : [a , b]rarr [1, infty] be a continuous function and let g : R ...

    Text Solution

    |

  14. The value of int0^1 4x^3 {d^2/(dx^2) (1 - x^2)^5 } dx is

    Text Solution

    |

  15. The following integral int(pi/4)^(pi/2) (2 cosec x)^17 dx is equal to

    Text Solution

    |

  16. Let f : [0,2] rarr R be a function which is continuous on [0 , 2] and ...

    Text Solution

    |

  17. Given that for each a in (0,1), underset(h rarr 0)(lim) inth^(1 - h)...

    Text Solution

    |

  18. Given that for each a in (0,1), underset(h rarr 0)(lim) inth^(1 - h)...

    Text Solution

    |

  19. Match List - I with List - II

    Text Solution

    |

  20. The integral int0^pi sqrt(1 + 4 sin^2(x/2) - 4 sin (x/2)) dx equals :

    Text Solution

    |