Home
Class 12
MATHS
Let f(x) be a continuous function which ...

Let `f(x)` be a continuous function which takes positive values for `xge0` and satisfy `int_(0)^(x)f(t)dt=x sqrt(f(x))` with `f(1)=1/2`. Then

A

`f(x)` is increasing function in domain

B

`f(x)` is decreasing function in domain

C

`f(sqrt(2)+1)=1/(2sqrt(2))`

D

`f(sqrt(2)+1)=1/4`

Text Solution

Verified by Experts

The correct Answer is:
B, D
`:'f(x)=(xf^(')(x))/(2sqrt(f(x)))+sqrt(f(x))`
`impliessqrt(f(x))=/(1-cx)`
`impliesf(x)=1/((1-cx)^(2))`
`:'f(1)=1/2 :.c=1-sqrt(2)`
`impliesf(x)=1/([1+(sqrt(2)-1)x]^(2))`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINE

    FIITJEE|Exercise NUMERICAL BASED|4 Videos

  • TIPS

    FIITJEE|Exercise NUERICAL DECIMAL BASED QUATIONS|20 Videos

Similar Questions

Explore conceptually related problems

Let f(x) is a continuous function which takes positive values for x>=0 and satisfy int_(0)^(x)f(t)dt=x sqrt(f(x)) with f(1)=1/2. Find the value of f(sqrt(2)+1)

Let f(x) be an odd continuous function which is periodic with period 2. if g(x)=int_(0)^(x) f(t)dt , then

Let f:R rarr R be a continuous function which satisfies f(x)=int_(0)^(x)f(t)dt. Then the value of f(1n5) is

Let f(x) be a continuous function defined from [0,2]rarr R and satisfying the equation int_(0)^(2)f(x)(x-f(x))dx=(2)/(3) then the value of 2f(1)

A continuous function f(x) satisfies the relation f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt then f(1)=

Let f be a continuous function on R and satisfies f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt, then which of the following is(are) correct?

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

Let f be a continuous function on (0,oo) and satisfying f(x)=(log_(e)x)^(2)-int_(1)^(e)(f(t))/(t)dt for all x>=1, then f(e) equals

FIITJEE-TEST PAPERS-MATHEMATICS
  1. In a /\ABC if a^(2)-b^(2)-c^(2)+(x-2)bc=0 then x be equal to

    Text Solution

    |

  2. If f(x)={b^(2)+(a-1)b+2}x-int(sin^(2)x+cos^(4)x)dx be an increasing fu...

    Text Solution

    |

  3. Let f(x) be a continuous function which takes positive values for xge0...

    Text Solution

    |

  4. If x+y=3 is tangent at (2,1) on hyperbola, intersects asymptotes at A ...

    Text Solution

    |

  5. If x^(2)+y^(2)=16 is director circle of locus of centre of a moving el...

    Text Solution

    |

  6. If theta is acute angle of intersect between two curves x^(2)+5y^(2)=6...

    Text Solution

    |

  7. If 8 harmonic means are inserted between two numbes a and b (altb) suc...

    Text Solution

    |

  8. If f(x)=sum(i=1)^(oo) x/({(i-1)x+1}(ix+1)), then f(2017)+f(1/2017) is ...

    Text Solution

    |

  9. If tangent is drawn at (x(1), y(1)) on the hyperbola (x^(2))/4-(y^(2))...

    Text Solution

    |

  10. If int(0)^(x)((t^(3)+t)dt)/((1+3t^(2)))=f(x), then int(0)^(1)f^(')(x) ...

    Text Solution

    |

  11. If y=f(x) is solution of differentiable equation (dy)/(dx)=y/x((1-3x^(...

    Text Solution

    |

  12. If 5x(1+ 1/(x^(2)+y^(2)))=12 and 5y(1- 1/(x^(2)+y^(2)))=4 AAx,yepsilon...

    Text Solution

    |

  13. If a tangent on ellipse at A(1,1) intersect its directrix at B(7,-6) a...

    Text Solution

    |

  14. let f(x)=(cos^-1(1-{x})sin^-1(1-{x}))/sqrt(2{x}(1-{x})) where {x} deno...

    Text Solution

    |

  15. If int(a)^(b)|sin|dx=8& int(0)^(a+b)|cosx|dx=9 ten

    Text Solution

    |

  16. If a,b,c are sides an acute angle triangle satisfying a^(2)+b^(2)+c^(2...

    Text Solution

    |

  17. If locus of point P(z) in complex plane ils |z+z(1)|+|z+z(2)|=4 where ...

    Text Solution

    |

  18. If locus of point P(z) in complex plane is |z+z(1)|+|z+z(2)|=4 where A...

    Text Solution

    |

  19. If f(2+x)+f(x)=2 for all xepsilon [0,2] and k=int(0)^(4)f(x)dx-4 such ...

    Text Solution

    |

  20. There are "n" married couples at a path each person shakes hand with e...

    Text Solution

    |