Home
Class 12
MATHS
Let a function f(x)s a t i sfi e sf(x)+f...

Let a function `f(x)s a t i sfi e sf(x)+f(2x)+f(2-x)+f(1+x)=AAx in Rdot` Then find the value of `f(0)dot`

Text Solution

Verified by Experts

`f(x) +f(2x)+f(2-x)+f(1+x)=x `
Put `x=0.` Then,
` f(0)+f(0)+f(2)+f(1)=0`
or `2f(0)+f(1)+f(2)=0 " (1)" `
Put `x=1`. Then,
`f(1)+f(2)+f(1)+f(2)=1`
` :. f(1)+f(2)=1//2`
So, from (1)
`2f(0)+1//2=0`
` :. f(0)= -1//4`
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE PUBLICATION|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Let a function f(x) satisfies f(x)+f(2x)+f(2-x)+f(1+x)=x ,AAx in Rdot Then find the value of f(0)dot

A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(x y)AAx , y in R and if f(2)=5, then find the value of f(f(2))dot

Determine the function satisfying f^2(x+y)=f^2(x)+f^2(y)AAx ,y in Rdot

Let f(x) be a differentiable function satisfying f(x)=int_(0)^(x)e^((2tx-t^(2)))cos(x-t)dt , then find the value of f''(0) .

Let f (x+(1)/(x))= x^(2) +(1)/(x^(2)) , x ne 0, then the value of f (x) is-

If f'(x)=f(x)+ int_(0)^(1)f(x)dx , given f(0)=1 , then find the value of f(log_(e)2) is

Let a function f(x), x ne 0 be such that f(x)+f((1)/(x))=f(x)*f((1)/(x))" then " f(x) can be

If the function f: R- {0}-> R given by f(x)=1/x-2/(e^(2x)-1) is continuous at x=0, then find the value of f(0)

If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, then find the value of int_0^a(dx)/(1+f(x))

CENGAGE PUBLICATION-RELATIONS AND FUNCTIONS-All Questions
  1. Let f(x)=x+f(x-1) for AAx in R. If f(0)=1,f i n d \ f(100).

    Text Solution

    |

  2. The function f(x) is defined for all real x. If f(a+b)=f(ab) AA a " a...

    Text Solution

    |

  3. Let a function f(x)s a t i sfi e sf(x)+f(2x)+f(2-x)+f(1+x)=AAx in Rdo...

    Text Solution

    |

  4. Let f be a function satisfying of xdot Then f(x y)=(f(x))/y for all po...

    Text Solution

    |

  5. If f(x) is a polynomial function satisfying f(x)dotf(1/x)=f(x)+f(1/x) ...

    Text Solution

    |

  6. Let f(x)=(9^x)/(9^x+3) . Show f(x)+f(1-x)=1 and, hence, evaluate. f(1/...

    Text Solution

    |

  7. Consider a real-valued function f(x) satisfying 2f(x y)=(f(x))^y+(f(y)...

    Text Solution

    |

  8. Let f be a real-valued function such that f(x)+2f((2002)/x)=3xdot Then...

    Text Solution

    |

  9. If f: R->R is an odd function such that f(1+x)=1+f(x)and x^2f(1/x)...

    Text Solution

    |

  10. Let f: R^+vecR be a function which satisfies f(x)dotf(y)=f(x y)+2(1/x+...

    Text Solution

    |

  11. A continuous function f(x)onR->R satisfies the relation f(x)+f(2x+y)+5...

    Text Solution

    |

  12. If for all real values of ua n dv ,2f(u)cosv=f(u+v)+f(u-v), prove that...

    Text Solution

    |

  13. Prove that f(x)gi v e nb yf(x+y)=f(x)+f(y)AAx in R is an odd function...

    Text Solution

    |

  14. If f(x+y)=f(x)dotf(y) for all real x , ya n df(0)!=0, then prove that ...

    Text Solution

    |

  15. Let f(x) be periodic and k be a positive real number such that f(x+k)+...

    Text Solution

    |

  16. If f(x) satisfies the relation f(x)+f(x+4)=f(x+2)+f(x+6) for allx , th...

    Text Solution

    |

  17. An odd function is symmetric about the vertical line x=a ,(a >0),a n d...

    Text Solution

    |

  18. Check whether the function defined by f(x+lambda)=1+sqrt(2f(x)-f^2(x))...

    Text Solution

    |

  19. Draw the graph of y=-log(e)x.

    Text Solution

    |

  20. Draw the graph of y=|||x|-2|-3| by transforming the graph of y=|x|

    Text Solution

    |