Home
Class 12
MATHS
For x in R, the functions f(x) satisfies...

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

A

`13/3`

B

`43/3`

C

`23/3`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 1|5 Videos

  • FUNCTIONS

    ARIHANT MATHS|Exercise Exercise For Session 2|6 Videos

  • ESSENTIAL MATHEMATICAL TOOLS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|3 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

Similar Questions

Explore conceptually related problems

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

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

If f(x)=(x-4)/(2sqrtx) , then f'(1) is equal to:

If f(x)=(x-4)/(2sqrt3) , then f'(1) is equal to?

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f'(0) is equal to

A function y-f (x) satisfies the differential equation f (x) sin 2x - cos x+(1+ sin ^(2)x) f'(x) =0 with f (0) =0. The value of f ((pi)/(6)) equals to :

If the functions f(x)=x^(3)+e^(x//2) " and " g(x)=f^(-1)(x) , the value of g'(1) is ………… .

Let the function f satisfies f(x).f ′ (−x)=f(−x).f ′ (x) for all x and f(0)=3 The value of f(x).f(-x) for all x is

Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4)=x^(2) . f(3) is equal to

ARIHANT MATHS-FUNCTIONS-Exercise (Questions Asked In Previous 13 Years Exam)
  1. For x in R, the functions f(x) satisfies 2f(x)+f(1-x)=x^(2). The value...

    Text Solution

    |

  2. If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x), then the value ...

    Text Solution

    |

  3. Let F(x) be an indefinite integral of sin^(2)x Statement-1: The fun...

    Text Solution

    |

  4. Find the range of values of t for which 2sint=(1-2x+5x^2)/(3x^2-2x-1)

    Text Solution

    |

  5. Let F(k)(x)=1/k (sin^(k)x+cos^(k)x), where x in R and k ge 1, then fin...

    Text Solution

    |

  6. Let f:R-R be defined as f(x) = x^4, then (a) f is one-one (b) f is man...

    Text Solution

    |

  7. Let f(x)=x^2a n dg(x)=sinx for all x in R Then the set of all x satis...

    Text Solution

    |

  8. Let f:(0,1)->R be defined by f(x)=(b-x)/(1-bx), where b is constant s...

    Text Solution

    |

  9. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  10. If X and Y are two non-empty sets where f: X->Y,is function is define...

    Text Solution

    |

  11. If f(x)={x, when x is rational and 0, when x is irrational g(x)={0, w...

    Text Solution

    |

  12. If f(x)=sinx+cosx, g(x)=x^(2)-1, then g(f(x)) is invertible in the do...

    Text Solution

    |

  13. The domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) ...

    Text Solution

    |

  14. The range of the function f(x)=(x^2+x+2)/(x^2+x+1),x in R , is (a) (...

    Text Solution

    |

  15. If f:[0,infty) rarr [0,infty) " and " f(x)=x/(1+x), then f is

    Text Solution

    |

  16. If f:R to R be defined by f(x) =2x+sinx for x in R, then check the na...

    Text Solution

    |

  17. Let E={1,2,3,4} and F={1,2}dot If N is the number of onto functions fr...

    Text Solution

    |

  18. Suppose f(x)=(x+1)^(2) " for " x ge -1. If g(x) is the function whos...

    Text Solution

    |

  19. If F :[1,oo)->[2,oo) is given by f(x)=x+1/x ,t h e n \ f^(-1)(x) equal...

    Text Solution

    |

  20. Let f(x)=(1+b^2)x^2+2b x+1 and let m(b) the minimum value of f(x)dot A...

    Text Solution

    |

  21. Find the domain of the following functions. f(x)=(log(2)(x+3))/((x^(...

    Text Solution

    |